LMFDB - Embedded newform 69.2.e.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	69.31
Dual form			69.2.e.b.49.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.357685 - 2.48775i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-4.14200 - 1.21620i) q^{4} +(2.65565 + 3.06479i) q^{5} +(-2.41153 + 0.708089i) q^{6} +(-1.15843 - 0.744479i) q^{7} +(-2.41899 + 5.29684i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.357685 - 2.48775i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-4.14200 - 1.21620i) q^{4} +(2.65565 + 3.06479i) q^{5} +(-2.41153 + 0.708089i) q^{6} +(-1.15843 - 0.744479i) q^{7} +(-2.41899 + 5.29684i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(8.57432 - 5.51038i) q^{10} +(-0.00388573 - 0.0270259i) q^{11} +(0.614354 + 4.27292i) q^{12} +(-0.527646 + 0.339098i) q^{13} +(-2.26643 + 2.61561i) q^{14} +(1.68463 - 3.68882i) q^{15} +(5.04885 + 3.24470i) q^{16} +(4.13515 - 1.21419i) q^{17} +(1.64589 + 1.89945i) q^{18} +(-4.79898 - 1.40911i) q^{19} +(-7.27232 - 15.9241i) q^{20} +(-0.195972 + 1.36301i) q^{21} -0.0686236 q^{22} +(1.11722 + 4.66388i) q^{23} +5.82306 q^{24} +(-1.62885 + 11.3289i) q^{25} +(0.654861 + 1.43394i) q^{26} +(0.959493 + 0.281733i) q^{27} +(3.89279 + 4.49252i) q^{28} +(-3.54487 + 1.04087i) q^{29} +(-8.57432 - 5.51038i) q^{30} +(-0.200359 + 0.438726i) q^{31} +(2.25133 - 2.59818i) q^{32} +(-0.0229694 + 0.0147615i) q^{33} +(-1.54152 - 10.7215i) q^{34} +(-0.794723 - 5.52742i) q^{35} +(3.63158 - 2.33387i) q^{36} +(1.44203 - 1.66419i) q^{37} +(-5.22204 + 11.4347i) q^{38} +(0.527646 + 0.339098i) q^{39} +(-22.6577 + 6.65289i) q^{40} +(-6.56243 - 7.57345i) q^{41} +(3.32075 + 0.975060i) q^{42} +(-1.36272 - 2.98394i) q^{43} +(-0.0167742 + 0.116667i) q^{44} -4.05529 q^{45} +(12.0022 - 1.11118i) q^{46} +8.98345 q^{47} +(0.854114 - 5.94049i) q^{48} +(-2.12019 - 4.64257i) q^{49} +(27.6009 + 8.10436i) q^{50} +(-2.82227 - 3.25707i) q^{51} +(2.59792 - 0.762819i) q^{52} +(1.54567 + 0.993342i) q^{53} +(1.04408 - 2.28621i) q^{54} +(0.0725093 - 0.0836802i) q^{55} +(6.74562 - 4.33514i) q^{56} +(0.711799 + 4.95067i) q^{57} +(1.32148 + 9.19107i) q^{58} +(-3.51609 + 2.25965i) q^{59} +(-11.4641 + 13.2303i) q^{60} +(1.92053 - 4.20538i) q^{61} +(1.01978 + 0.655371i) q^{62} +(1.32125 - 0.387954i) q^{63} +(2.20204 + 2.54129i) q^{64} +(-2.44051 - 0.716597i) q^{65} +(0.0285073 + 0.0624222i) q^{66} +(-0.630353 + 4.38420i) q^{67} -18.6045 q^{68} +(3.77831 - 2.95371i) q^{69} -14.0351 q^{70} +(1.02832 - 7.15212i) q^{71} +(-2.41899 - 5.29684i) q^{72} +(-5.72936 - 1.68229i) q^{73} +(-3.62430 - 4.18266i) q^{74} +(10.9818 - 3.22454i) q^{75} +(18.1636 + 11.6731i) q^{76} +(-0.0156188 + 0.0342005i) q^{77} +(1.03232 - 1.19136i) q^{78} +(1.26938 - 0.815780i) q^{79} +(3.46368 + 24.0904i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-21.1882 + 13.6168i) q^{82} +(5.61081 - 6.47522i) q^{83} +(2.46941 - 5.40726i) q^{84} +(14.7027 + 9.44888i) q^{85} +(-7.91074 + 2.32280i) q^{86} +(2.41940 + 2.79213i) q^{87} +(0.152551 + 0.0447931i) q^{88} +(5.53741 + 12.1252i) q^{89} +(-1.45052 + 10.0886i) q^{90} +0.863693 q^{91} +(1.04468 - 20.6766i) q^{92} +0.482312 q^{93} +(3.21325 - 22.3486i) q^{94} +(-8.42581 - 18.4500i) q^{95} +(-3.29862 - 0.968563i) q^{96} +(-1.41765 - 1.63606i) q^{97} +(-12.3079 + 3.61394i) q^{98} +(0.0229694 + 0.0147615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.357685	−	2.48775i	0.252922	−	1.75911i	−0.327556	−	0.944832i	$-0.606225\pi$
$2$	0.357685	−	2.48775i	0.252922	−	1.75911i	0.580477	−	0.814276i	$-0.302866\pi$
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−4.14200	−	1.21620i	−2.07100	−	0.608100i
$5$	2.65565	+	3.06479i	1.18764	+	1.37061i	0.912431	+	0.409230i	$0.134203\pi$
$5$	2.65565	+	3.06479i	1.18764	+	1.37061i	0.275213	+	0.961383i	$0.411252\pi$
$6$	−2.41153	+	0.708089i	−0.984503	+	0.289076i
$7$	−1.15843	−	0.744479i	−0.437846	−	0.281387i	0.303090	−	0.952962i	$-0.401982\pi$
$7$	−1.15843	−	0.744479i	−0.437846	−	0.281387i	−0.740936	+	0.671575i	$0.765618\pi$
$8$	−2.41899	+	5.29684i	−0.855241	+	1.87272i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	8.57432	−	5.51038i	2.71144	−	1.74254i
$11$	−0.00388573	−	0.0270259i	−0.00117159	−	0.00814861i	0.989227	−	0.146388i	$-0.0467648\pi$
$11$	−0.00388573	−	0.0270259i	−0.00117159	−	0.00814861i	−0.990399	+	0.138239i	$0.955856\pi$
$12$	0.614354	+	4.27292i	0.177349	+	1.23349i
$13$	−0.527646	+	0.339098i	−0.146343	+	0.0940488i	−0.611763	−	0.791041i	$-0.709539\pi$
$13$	−0.527646	+	0.339098i	−0.146343	+	0.0940488i	0.465420	+	0.885090i	$0.345903\pi$
$14$	−2.26643	+	2.61561i	−0.605730	+	0.699050i
$15$	1.68463	−	3.68882i	0.434969	−	0.952450i
$16$	5.04885	+	3.24470i	1.26221	+	0.811175i
$17$	4.13515	−	1.21419i	1.00292	−	0.294484i	0.261267	−	0.965267i	$-0.415860\pi$
$17$	4.13515	−	1.21419i	1.00292	−	0.294484i	0.741654	+	0.670783i	$0.234042\pi$
$18$	1.64589	+	1.89945i	0.387939	+	0.447705i
$19$	−4.79898	−	1.40911i	−1.10096	−	0.323272i	−0.319728	−	0.947509i	$-0.603591\pi$
$19$	−4.79898	−	1.40911i	−1.10096	−	0.323272i	−0.781234	+	0.624238i	$0.785410\pi$
$20$	−7.27232	−	15.9241i	−1.62614	−	3.56075i
$21$	−0.195972	+	1.36301i	−0.0427646	+	0.297434i
$22$	−0.0686236			−0.0146306
$23$	1.11722	+	4.66388i	0.232957	+	0.972487i
$23$	1.11722	+	4.66388i	0.232957	+	0.972487i
$24$	5.82306			1.18863
$25$	−1.62885	+	11.3289i	−0.325770	+	2.26578i
$26$	0.654861	+	1.43394i	0.128429	+	0.281220i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	3.89279	+	4.49252i	0.735668	+	0.849006i
$29$	−3.54487	+	1.04087i	−0.658266	+	0.193284i	−0.593771	−	0.804634i	$-0.702362\pi$
$29$	−3.54487	+	1.04087i	−0.658266	+	0.193284i	−0.0644943	+	0.997918i	$0.520543\pi$
$30$	−8.57432	−	5.51038i	−1.56545	−	1.00605i
$31$	−0.200359	+	0.438726i	−0.0359856	+	0.0787975i	−0.926771	−	0.375626i	$-0.877428\pi$
$31$	−0.200359	+	0.438726i	−0.0359856	+	0.0787975i	0.890786	+	0.454424i	$0.150155\pi$
$32$	2.25133	−	2.59818i	0.397983	−	0.459297i
$33$	−0.0229694	+	0.0147615i	−0.00399846	+	0.00256965i
$34$	−1.54152	−	10.7215i	−0.264369	−	1.83873i
$35$	−0.794723	−	5.52742i	−0.134333	−	0.934305i
$36$	3.63158	−	2.33387i	0.605263	−	0.388979i
$37$	1.44203	−	1.66419i	0.237067	−	0.273590i	−0.624732	−	0.780839i	$-0.714792\pi$
$37$	1.44203	−	1.66419i	0.237067	−	0.273590i	0.861800	+	0.507249i	$0.169337\pi$
$38$	−5.22204	+	11.4347i	−0.847127	+	1.85495i
$39$	0.527646	+	0.339098i	0.0844910	+	0.0542991i
$40$	−22.6577	+	6.65289i	−3.58249	+	1.05191i
$41$	−6.56243	−	7.57345i	−1.02488	−	1.18277i	−0.982991	−	0.183652i	$-0.941208\pi$
$41$	−6.56243	−	7.57345i	−1.02488	−	1.18277i	−0.0418888	−	0.999122i	$-0.513338\pi$
$42$	3.32075	+	0.975060i	0.512403	+	0.150455i
$43$	−1.36272	−	2.98394i	−0.207813	−	0.455047i	0.776811	−	0.629734i	$-0.216836\pi$
$43$	−1.36272	−	2.98394i	−0.207813	−	0.455047i	−0.984624	+	0.174687i	$0.944109\pi$
$44$	−0.0167742	+	0.116667i	−0.00252880	+	0.0175882i
$45$	−4.05529			−0.604527
$46$	12.0022	−	1.11118i	1.76963	−	0.163834i
$47$	8.98345			1.31037			0.655186	−	0.755468i	$-0.272590\pi$
$47$	8.98345			1.31037			0.655186	+	0.755468i	$0.272590\pi$
$48$	0.854114	−	5.94049i	0.123281	−	0.857437i
$49$	−2.12019	−	4.64257i	−0.302884	−	0.663224i
$50$	27.6009	+	8.10436i	3.90336	+	1.14613i
$51$	−2.82227	−	3.25707i	−0.395196	−	0.456081i
$52$	2.59792	−	0.762819i	0.360267	−	0.105784i
$53$	1.54567	+	0.993342i	0.212314	+	0.136446i	0.642476	−	0.766306i	$-0.277907\pi$
$53$	1.54567	+	0.993342i	0.212314	+	0.136446i	−0.430162	+	0.902752i	$0.641544\pi$
$54$	1.04408	−	2.28621i	0.142081	−	0.311114i
$55$	0.0725093	−	0.0836802i	0.00977716	−	0.0112834i
$56$	6.74562	−	4.33514i	0.901421	−	0.579308i
$57$	0.711799	+	4.95067i	0.0942801	+	0.655733i
$58$	1.32148	+	9.19107i	0.173518	+	1.20685i
$59$	−3.51609	+	2.25965i	−0.457756	+	0.294182i	−0.749125	−	0.662429i	$-0.769526\pi$
$59$	−3.51609	+	2.25965i	−0.457756	+	0.294182i	0.291369	+	0.956611i	$0.405889\pi$
$60$	−11.4641	+	13.2303i	−1.48001	+	1.70802i
$61$	1.92053	−	4.20538i	0.245899	−	0.538444i	−0.745929	−	0.666025i	$-0.767994\pi$
$61$	1.92053	−	4.20538i	0.245899	−	0.538444i	0.991828	+	0.127582i	$0.0407215\pi$
$62$	1.01978	+	0.655371i	0.129512	+	0.0832322i
$63$	1.32125	−	0.387954i	0.166462	−	0.0488776i
$64$	2.20204	+	2.54129i	0.275255	+	0.317661i
$65$	−2.44051	−	0.716597i	−0.302708	−	0.0888830i
$66$	0.0285073	+	0.0624222i	0.00350900	+	0.00768365i
$67$	−0.630353	+	4.38420i	−0.0770099	+	0.535616i	0.914399	+	0.404815i	$0.132664\pi$
$67$	−0.630353	+	4.38420i	−0.0770099	+	0.535616i	−0.991409	+	0.130801i	$0.958245\pi$
$68$	−18.6045			−2.25612
$69$	3.77831	−	2.95371i	0.454855	−	0.355585i
$70$	−14.0351			−1.67752
$71$	1.02832	−	7.15212i	0.122039	−	0.848801i	−0.833201	−	0.552970i	$-0.813494\pi$
$71$	1.02832	−	7.15212i	0.122039	−	0.848801i	0.955240	−	0.295831i	$-0.0955965\pi$
$72$	−2.41899	−	5.29684i	−0.285080	−	0.624239i
$73$	−5.72936	−	1.68229i	−0.670571	−	0.196898i	−0.0713140	−	0.997454i	$-0.522719\pi$
$73$	−5.72936	−	1.68229i	−0.670571	−	0.196898i	−0.599257	+	0.800556i	$0.704537\pi$
$74$	−3.62430	−	4.18266i	−0.421316	−	0.486224i
$75$	10.9818	−	3.22454i	1.26807	−	0.372338i
$76$	18.1636	+	11.6731i	2.08351	+	1.33899i
$77$	−0.0156188	+	0.0342005i	−0.00177993	+	0.00389751i
$78$	1.03232	−	1.19136i	0.116888	−	0.134895i
$79$	1.26938	−	0.815780i	0.142816	−	0.0917824i	−0.467281	−	0.884109i	$-0.654767\pi$
$79$	1.26938	−	0.815780i	0.142816	−	0.0917824i	0.610098	+	0.792326i	$0.291130\pi$
$80$	3.46368	+	24.0904i	0.387252	+	2.69339i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−21.1882	+	13.6168i	−2.33984	+	1.50373i
$83$	5.61081	−	6.47522i	0.615866	−	0.710748i	−0.359050	−	0.933318i	$-0.616899\pi$
$83$	5.61081	−	6.47522i	0.615866	−	0.710748i	0.974917	+	0.222570i	$0.0714447\pi$
$84$	2.46941	−	5.40726i	0.269435	−	0.589981i
$85$	14.7027	+	9.44888i	1.59474	+	1.02487i
$86$	−7.91074	+	2.32280i	−0.853037	+	0.250474i
$87$	2.41940	+	2.79213i	0.259387	+	0.299348i
$88$	0.152551	+	0.0447931i	0.0162620	+	0.00477496i
$89$	5.53741	+	12.1252i	0.586965	+	1.28527i	0.937259	+	0.348634i	$0.113354\pi$
$89$	5.53741	+	12.1252i	0.586965	+	1.28527i	−0.350295	+	0.936640i	$0.613919\pi$
$90$	−1.45052	+	10.0886i	−0.152898	+	1.06343i
$91$	0.863693			0.0905397
$92$	1.04468	−	20.6766i	0.108916	−	2.15568i
$93$	0.482312			0.0500134
$94$	3.21325	−	22.3486i	0.331421	−	2.30509i
$95$	−8.42581	−	18.4500i	−0.864470	−	1.89293i
$96$	−3.29862	−	0.968563i	−0.336664	−	0.0988536i
$97$	−1.41765	−	1.63606i	−0.143941	−	0.166117i	0.679201	−	0.733952i	$-0.262326\pi$
$97$	−1.41765	−	1.63606i	−0.143941	−	0.166117i	−0.823142	+	0.567835i	$0.807781\pi$
$98$	−12.3079	+	3.61394i	−1.24329	+	0.365063i
$99$	0.0229694	+	0.0147615i	0.00230851	+	0.00148359i
$100$	20.5249	−	44.9433i	2.05249	−	4.49433i
$101$	−8.74204	+	10.0889i	−0.869866	+	1.00388i	0.130058	+	0.991506i	$0.458484\pi$
$101$	−8.74204	+	10.0889i	−0.869866	+	1.00388i	−0.999923	+	0.0123724i	$0.996062\pi$
$102$	−9.11228	+	5.85610i	−0.902250	+	0.579841i
$103$	−1.34518	−	9.35596i	−0.132545	−	0.921870i	−0.942221	−	0.334993i	$-0.891266\pi$
$103$	−1.34518	−	9.35596i	−0.132545	−	0.921870i	0.809676	−	0.586877i	$-0.199643\pi$
$104$	−0.519777	−	3.61513i	−0.0509684	−	0.354493i
$105$	−4.69778	+	3.01908i	−0.458456	+	0.294632i
$106$	3.02406	−	3.48995i	0.293722	−	0.338974i
$107$	−5.72839	+	12.5434i	−0.553785	+	1.21262i	0.401207	+	0.915987i	$0.368591\pi$
$107$	−5.72839	+	12.5434i	−0.553785	+	1.21262i	−0.954992	+	0.296632i	$0.904137\pi$
$108$	−3.63158	−	2.33387i	−0.349449	−	0.224577i
$109$	7.83275	−	2.29990i	0.750242	−	0.220291i	0.115812	−	0.993271i	$-0.463053\pi$
$109$	7.83275	−	2.29990i	0.750242	−	0.220291i	0.634430	+	0.772980i	$0.281235\pi$
$110$	−0.182240	−	0.210317i	−0.0173759	−	0.0200529i
$111$	−2.11284	−	0.620384i	−0.200541	−	0.0588843i
$112$	−3.43314	−	7.51753i	−0.324401	−	0.710340i
$113$	2.08128	−	14.4756i	0.195790	−	1.36175i	−0.620545	−	0.784171i	$-0.713089\pi$
$113$	2.08128	−	14.4756i	0.195790	−	1.36175i	0.816335	−	0.577578i	$-0.196002\pi$
$114$	12.5707			1.17735
$115$	−11.3268	+	15.8097i	−1.05623	+	1.47426i
$116$	15.9488			1.48080
$117$	0.0892619	−	0.620830i	0.00825227	−	0.0573958i
$118$	4.36381	+	9.55541i	0.401721	+	0.879647i
$119$	−5.69422	−	1.67197i	−0.521989	−	0.153270i
$120$	15.4640	+	17.8464i	1.41167	+	1.62915i
$121$	10.5537	−	3.09885i	0.959428	−	0.281713i
$122$	−9.77501	−	6.28201i	−0.884987	−	0.568747i
$123$	−4.16292	+	9.11553i	−0.375358	+	0.821919i
$124$	1.36347	−	1.57353i	0.122443	−	0.141307i
$125$	−21.9887	+	14.1313i	−1.96673	+	1.26394i
$126$	−0.492543	−	3.42571i	−0.0438792	−	0.305187i
$127$	−0.258432	−	1.79743i	−0.0229321	−	0.159496i	0.975138	−	0.221600i	$-0.0711281\pi$
$127$	−0.258432	−	1.79743i	−0.0229321	−	0.159496i	−0.998070	+	0.0621040i	$0.980219\pi$
$128$	12.8940	−	8.28647i	1.13968	−	0.732428i
$129$	−2.14820	+	2.47915i	−0.189138	+	0.218277i
$130$	−2.65565	+	5.81507i	−0.232916	+	0.510015i
$131$	4.99336	+	3.20904i	0.436272	+	0.280375i	0.740285	−	0.672293i	$-0.234690\pi$
$131$	4.99336	+	3.20904i	0.436272	+	0.280375i	−0.304013	+	0.952668i	$0.598327\pi$
$132$	0.113092	−	0.0332069i	0.00984342	−	0.00289029i
$133$	4.51024	+	5.20510i	0.391088	+	0.451339i
$134$	10.6814	+	3.13633i	0.922728	+	0.270938i
$135$	1.68463	+	3.68882i	0.144990	+	0.317483i
$136$	−3.57150	+	24.8403i	−0.306254	+	2.13004i
$137$	8.05383			0.688085			0.344043	−	0.938954i	$-0.388204\pi$
$137$	8.05383			0.688085			0.344043	+	0.938954i	$0.388204\pi$
$138$	−5.99666	−	10.4560i	−0.510470	−	0.890074i
$139$	−7.68012			−0.651419			−0.325709	−	0.945470i	$-0.605603\pi$
$139$	−7.68012			−0.651419			−0.325709	+	0.945470i	$0.605603\pi$
$140$	−3.43071	+	23.8611i	−0.289948	+	2.01663i
$141$	−3.73186	−	8.17164i	−0.314279	−	0.688176i
$142$	−17.4249	−	5.11642i	−1.46227	−	0.429360i
$143$	0.0112147	+	0.0129425i	0.000937821	+	0.00108230i
$144$	−5.75848	+	1.69084i	−0.479873	+	0.140903i
$145$	−12.6040	−	8.10008i	−1.04670	−	0.672675i
$146$	−6.23444	+	13.6515i	−0.515966	+	1.12981i
$147$	−3.34227	+	3.85719i	−0.275666	+	0.318135i
$148$	−7.99685	+	5.13926i	−0.657337	+	0.422445i
$149$	0.411897	+	2.86481i	0.0337439	+	0.234694i	0.999713	−	0.0239640i	$-0.00762872\pi$
$149$	0.411897	+	2.86481i	0.0337439	+	0.234694i	−0.965969	+	0.258658i	$0.916720\pi$
$150$	−4.09385	−	28.4733i	−0.334261	−	2.32484i
$151$	1.73780	−	1.11682i	0.141420	−	0.0908852i	−0.468018	−	0.883719i	$-0.655032\pi$
$151$	1.73780	−	1.11682i	0.141420	−	0.0908852i	0.609438	+	0.792834i	$0.291395\pi$
$152$	19.0725	−	22.0108i	1.54698	−	1.78531i
$153$	−1.79032	+	3.92026i	−0.144739	+	0.316934i
$154$	0.0794958	+	0.0510888i	0.00640595	+	0.00411685i
$155$	−1.87669	+	0.551045i	−0.150739	+	0.0442610i
$156$	−1.77310	−	2.04627i	−0.141962	−	0.163832i
$157$	18.5997	+	5.46138i	1.48442	+	0.435865i	0.920756	−	0.390138i	$-0.127573\pi$
$157$	18.5997	+	5.46138i	1.48442	+	0.435865i	0.563665	+	0.826003i	$0.309391\pi$
$158$	−1.57542	−	3.44970i	−0.125334	−	0.274443i
$159$	0.261481	−	1.81864i	0.0207368	−	0.144228i
$160$	13.9416			1.10218
$161$	2.17794	−	6.23454i	0.171645	−	0.491351i
$162$	−2.51334			−0.197466
$163$	−3.33835	+	23.2187i	−0.261480	+	1.81863i	0.260273	+	0.965535i	$0.416188\pi$
$163$	−3.33835	+	23.2187i	−0.261480	+	1.81863i	−0.521753	+	0.853097i	$0.674722\pi$
$164$	17.9708	+	39.3505i	1.40328	+	3.07276i
$165$	−0.106240	−	0.0311948i	−0.00827075	−	0.00242851i
$166$	−14.1019	−	16.2744i	−1.09452	−	1.26314i
$167$	19.9215	−	5.84948i	1.54157	−	0.452647i	0.603004	−	0.797738i	$-0.293970\pi$
$167$	19.9215	−	5.84948i	1.54157	−	0.452647i	0.938569	+	0.345092i	$0.112152\pi$
$168$	−6.74562	−	4.33514i	−0.520436	−	0.334464i
$169$	−5.23697	+	11.4674i	−0.402844	+	0.882105i
$170$	28.7654	−	33.1971i	2.20621	−	2.54610i
$171$	4.20760	−	2.70406i	0.321763	−	0.206785i
$172$	2.01532	+	14.0168i	0.153666	+	1.06877i
$173$	0.510183	+	3.54840i	0.0387885	+	0.269780i	0.999981	−	0.00609715i	$-0.00194080\pi$
$173$	0.510183	+	3.54840i	0.0387885	+	0.269780i	−0.961193	+	0.275877i	$0.911032\pi$
$174$	7.81153	−	5.02016i	0.592190	−	0.380578i
$175$	10.3210	−	11.9111i	0.780197	−	0.900396i
$176$	0.0680724	−	0.149058i	0.00513115	−	0.0112356i
$177$	3.51609	+	2.25965i	0.264285	+	0.169846i
$178$	32.1453	−	9.43871i	2.40939	−	0.707461i
$179$	13.5335	+	15.6184i	1.01154	+	1.16738i	0.985837	+	0.167707i	$0.0536363\pi$
$179$	13.5335	+	15.6184i	1.01154	+	1.16738i	0.0257010	+	0.999670i	$0.491818\pi$
$180$	16.7970	+	4.93205i	1.25198	+	0.367613i
$181$	−10.7612	−	23.5637i	−0.799873	−	1.75148i	−0.645929	−	0.763397i	$-0.723530\pi$
$181$	−10.7612	−	23.5637i	−0.799873	−	1.75148i	−0.153943	−	0.988080i	$-0.549197\pi$
$182$	0.308930	−	2.14866i	0.0228994	−	0.159269i
$183$	−4.62316			−0.341754
$184$	−27.4064	−	5.36412i	−2.02043	−	0.395448i
$185$	8.92989			0.656539
$186$	0.172516	−	1.19987i	0.0126495	−	0.0879790i
$187$	−0.0488826	−	0.107038i	−0.00357465	−	0.00782739i
$188$	−37.2095	−	10.9257i	−2.71378	−	0.796837i
$189$	−0.901763	−	1.04069i	−0.0655936	−	0.0756991i
$190$	−48.9128	+	14.3621i	−3.54850	+	1.04193i
$191$	−6.97368	−	4.48171i	−0.504598	−	0.324285i	0.263455	−	0.964672i	$-0.415138\pi$
$191$	−6.97368	−	4.48171i	−0.504598	−	0.324285i	−0.768053	+	0.640386i	$0.778774\pi$
$192$	1.39688	−	3.05874i	0.100811	−	0.220745i
$193$	11.1106	−	12.8223i	0.799756	−	0.922967i	−0.198612	−	0.980078i	$-0.563643\pi$
$193$	11.1106	−	12.8223i	0.799756	−	0.922967i	0.998368	+	0.0571110i	$0.0181889\pi$
$194$	−4.57719	+	2.94158i	−0.328623	+	0.211193i
$195$	0.361983	+	2.51765i	0.0259222	+	0.180293i
$196$	3.13553	+	21.8081i	0.223966	+	1.55772i
$197$	−11.4221	+	7.34055i	−0.813792	+	0.522992i	−0.880090	−	0.474808i	$-0.842518\pi$
$197$	−11.4221	+	7.34055i	−0.813792	+	0.522992i	0.0662977	+	0.997800i	$0.478881\pi$
$198$	0.0449389	−	0.0518623i	0.00319367	−	0.00368569i
$199$	−5.33322	+	11.6781i	−0.378062	+	0.827840i	0.620969	+	0.783835i	$0.286739\pi$
$199$	−5.33322	+	11.6781i	−0.378062	+	0.827840i	−0.999031	+	0.0440054i	$0.985988\pi$
$200$	−56.0672	−	36.0322i	−3.96455	−	2.54786i
$201$	4.24987	−	1.24787i	0.299763	−	0.0880183i
$202$	21.9717	+	25.3567i	1.54592	+	1.78409i
$203$	4.88139	+	1.43331i	0.342607	+	0.100598i
$204$	7.72858	+	16.9232i	0.541109	+	1.18486i
$205$	5.78347	−	40.2249i	0.403935	−	2.80943i
$206$	−23.7565			−1.65519
$207$	−4.25635	−	2.20985i	−0.295837	−	0.153595i
$208$	−3.76428			−0.261006
$209$	−0.0194348	+	0.135172i	−0.00134433	+	0.00935005i
$210$	5.83040	+	12.7668i	0.402336	+	0.880993i
$211$	1.29335	+	0.379761i	0.0890377	+	0.0261438i	0.325948	−	0.945388i	$-0.394317\pi$
$211$	1.29335	+	0.379761i	0.0890377	+	0.0261438i	−0.236910	+	0.971532i	$0.576135\pi$
$212$	−5.19406	−	5.99427i	−0.356730	−	0.411688i
$213$	−6.93298	+	2.03571i	−0.475040	+	0.139484i
$214$	29.1560	+	18.7374i	1.99306	+	1.28086i
$215$	5.52623	−	12.1008i	0.376886	−	0.825265i
$216$	−3.81329	+	4.40077i	−0.259462	+	0.299435i
$217$	0.558725	−	0.359071i	0.0379287	−	0.0243753i
$218$	−2.91994	−	20.3086i	−0.197763	−	1.37547i
$219$	0.849796	+	5.91046i	0.0574239	+	0.399392i
$220$	−0.402106	+	0.258418i	−0.0271100	+	0.0174225i
$221$	−1.77017	+	2.04288i	−0.119074	+	0.137419i
$222$	−2.29909	+	5.03431i	−0.154305	+	0.337881i
$223$	−19.6245	−	12.6119i	−1.31415	−	0.844555i	−0.319476	−	0.947594i	$-0.603507\pi$
$223$	−19.6245	−	12.6119i	−1.31415	−	0.844555i	−0.994677	+	0.103039i	$0.967143\pi$
$224$	−4.54231	+	1.33374i	−0.303496	+	0.0891143i
$225$	−7.49514	−	8.64986i	−0.499676	−	0.576657i
$226$	−35.2673	−	10.3554i	−2.34594	−	0.688831i
$227$	2.54103	+	5.56408i	0.168654	+	0.369301i	0.975020	−	0.222116i	$-0.0712962\pi$
$227$	2.54103	+	5.56408i	0.168654	+	0.369301i	−0.806366	+	0.591416i	$0.798569\pi$
$228$	3.07274	−	21.3714i	0.203497	−	1.41535i
$229$	13.7597			0.909269			0.454635	−	0.890678i	$-0.349770\pi$
$229$	13.7597			0.909269			0.454635	+	0.890678i	$0.349770\pi$
$230$	35.2792	+	33.8333i	2.32624	+	2.23090i
$231$	0.0375981			0.00247378
$232$	3.06168	−	21.2944i	0.201009	−	1.39805i
$233$	5.88397	+	12.8841i	0.385472	+	0.844065i	0.998539	+	0.0540345i	$0.0172081\pi$
$233$	5.88397	+	12.8841i	0.385472	+	0.844065i	−0.613067	+	0.790031i	$0.710065\pi$
$234$	−1.51255	−	0.444124i	−0.0988782	−	0.0290333i
$235$	23.8569	+	27.5324i	1.55625	+	1.79601i
$236$	17.3118	−	5.08321i	1.12690	−	0.330889i
$237$	−1.26938	−	0.815780i	−0.0824550	−	0.0529906i
$238$	−6.19620	+	13.5678i	−0.401640	+	0.879469i
$239$	−13.3179	+	15.3697i	−0.861465	+	0.994183i	0.138528	+	0.990359i	$0.455763\pi$
$239$	−13.3179	+	15.3697i	−0.861465	+	0.994183i	−0.999993	+	0.00382482i	$0.998783\pi$
$240$	20.4746	−	13.1582i	1.32163	−	0.849359i
$241$	−1.11118	−	7.72840i	−0.0715772	−	0.497830i	−0.993801	−	0.111174i	$-0.964539\pi$
$241$	−1.11118	−	7.72840i	−0.0715772	−	0.497830i	0.922224	−	0.386657i	$-0.126370\pi$
$242$	−3.93427	−	27.3634i	−0.252904	−	1.75899i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−13.0694	+	15.0829i	−0.836684	+	0.965585i
$245$	8.59799	−	18.8270i	0.549305	−	1.20281i
$246$	21.1882	+	13.6168i	1.35091	+	0.868177i
$247$	3.00999	−	0.883813i	0.191521	−	0.0562357i
$248$	−1.83920	−	2.12254i	−0.116789	−	0.134782i
$249$	−8.22088	−	2.41387i	−0.520977	−	0.152973i
$250$	27.2901	+	59.7570i	1.72598	+	3.77936i
$251$	−2.12432	+	14.7750i	−0.134086	+	0.932587i	0.806065	+	0.591827i	$0.201593\pi$
$251$	−2.12432	+	14.7750i	−0.134086	+	0.932587i	−0.940151	+	0.340759i	$0.889316\pi$
$252$	−5.94445			−0.374465
$253$	0.121704	−	0.0483165i	0.00765148	−	0.00303763i
$254$	−4.56401			−0.286372
$255$	2.48726	−	17.2993i	0.155758	−	1.08332i
$256$	−13.2090	−	28.9236i	−0.825560	−	1.80772i
$257$	−13.0843	−	3.84190i	−0.816177	−	0.239651i	−0.153108	−	0.988209i	$-0.548928\pi$
$257$	−13.0843	−	3.84190i	−0.816177	−	0.239651i	−0.663069	+	0.748558i	$0.730746\pi$
$258$	5.39914	+	6.23094i	0.336136	+	0.387921i
$259$	−2.90944	+	0.854288i	−0.180784	+	0.0530829i
$260$	9.23705	+	5.93629i	0.572858	+	0.368153i
$261$	1.53476	−	3.36066i	0.0949993	−	0.208019i
$262$	9.76935	−	11.2744i	0.603553	−	0.696537i
$263$	5.98538	−	3.84657i	0.369075	−	0.237190i	−0.342936	−	0.939359i	$-0.611421\pi$
$263$	5.98538	−	3.84657i	0.369075	−	0.237190i	0.712010	+	0.702169i	$0.247785\pi$
$264$	−0.0226269	−	0.157373i	−0.00139259	−	0.00968565i
$265$	1.06038	+	7.37512i	0.0651388	+	0.453050i
$266$	14.5623	−	9.35859i	0.892869	−	0.573812i
$267$	8.72918	−	10.0740i	0.534217	−	0.616520i
$268$	7.94299	−	17.3927i	0.485196	−	1.06243i
$269$	−11.9712	−	7.69340i	−0.729894	−	0.469075i	0.122172	−	0.992509i	$-0.461014\pi$
$269$	−11.9712	−	7.69340i	−0.729894	−	0.469075i	−0.852066	+	0.523434i	$0.824651\pi$
$270$	9.77946	−	2.87151i	0.595159	−	0.174754i
$271$	−5.31964	−	6.13920i	−0.323145	−	0.372930i	0.570813	−	0.821080i	$-0.306628\pi$
$271$	−5.31964	−	6.13920i	−0.323145	−	0.372930i	−0.893958	+	0.448151i	$0.852083\pi$
$272$	24.8174	+	7.28705i	1.50478	+	0.441843i
$273$	−0.358791	−	0.785643i	−0.0217150	−	0.0475493i
$274$	2.88074	−	20.0360i	0.174032	−	1.21042i
$275$	0.312503			0.0188446
$276$	−19.2421	+	7.63908i	−1.15824	+	0.459819i
$277$	−3.71245			−0.223060			−0.111530	−	0.993761i	$-0.535575\pi$
$277$	−3.71245			−0.223060			−0.111530	+	0.993761i	$0.535575\pi$
$278$	−2.74706	+	19.1062i	−0.164758	+	1.14592i
$279$	−0.200359	−	0.438726i	−0.0119952	−	0.0262658i
$280$	31.2003	+	9.16123i	1.86457	+	0.547488i
$281$	−8.20261	−	9.46632i	−0.489327	−	0.564713i	0.456359	−	0.889796i	$-0.349153\pi$
$281$	−8.20261	−	9.46632i	−0.489327	−	0.564713i	−0.945686	+	0.325083i	$0.894608\pi$
$282$	−21.6639	+	6.36108i	−1.29006	+	0.378797i
$283$	−20.5721	−	13.2209i	−1.22289	−	0.785901i	−0.240118	−	0.970744i	$-0.577186\pi$
$283$	−20.5721	−	13.2209i	−1.22289	−	0.785901i	−0.982768	+	0.184842i	$0.940823\pi$
$284$	−12.9577	+	28.3735i	−0.768899	+	1.68365i
$285$	−13.2825	+	15.3288i	−0.786785	+	0.907998i
$286$	0.0362090	−	0.0232701i	0.00214108	−	0.00137599i
$287$	1.96386	+	13.6589i	0.115923	+	0.806261i
$288$	0.489262	+	3.40289i	0.0288300	+	0.200517i
$289$	1.32388	−	0.850806i	0.0778753	−	0.0500474i
$290$	−24.6593	+	28.4583i	−1.44804	+	1.67113i
$291$	−0.899298	+	1.96919i	−0.0527178	+	0.115436i
$292$	21.6850	+	13.9361i	1.26902	+	0.815550i
$293$	16.3811	−	4.80992i	0.956993	−	0.280999i	0.234297	−	0.972165i	$-0.424721\pi$
$293$	16.3811	−	4.80992i	0.956993	−	0.280999i	0.722696	+	0.691166i	$0.242903\pi$
$294$	8.40025	+	9.69441i	0.489913	+	0.565389i
$295$	−16.2629	−	4.77521i	−0.946860	−	0.278023i
$296$	5.32669	+	11.6638i	0.309607	+	0.677946i
$297$	0.00388573	−	0.0270259i	0.000225473	−	0.00156820i
$298$	7.27427			0.421387
$299$	−2.17101	−	2.08203i	−0.125553	−	0.120407i
$300$	−49.4082			−2.85258
$301$	−0.642863	+	4.47121i	−0.0370540	+	0.257716i
$302$	−2.15678	−	4.72269i	−0.124109	−	0.271760i
$303$	12.8087	+	3.76098i	0.735842	+	0.216063i
$304$	−19.6572	−	22.6856i	−1.12742	−	1.30111i
$305$	17.9888	−	5.28200i	1.03004	−	0.302447i
$306$	9.11228	+	5.85610i	0.520914	+	0.334771i
$307$	9.16309	−	20.0644i	0.522965	−	1.14513i	−0.445340	−	0.895362i	$-0.646917\pi$
$307$	9.16309	−	20.0644i	0.522965	−	1.14513i	0.968305	−	0.249772i	$-0.0803556\pi$
$308$	0.106288	−	0.122663i	0.00605631	−	0.00698936i
$309$	−7.95167	+	5.11023i	−0.452355	+	0.290711i
$310$	0.699602	+	4.86584i	0.0397347	+	0.276361i
$311$	0.775655	+	5.39480i	0.0439833	+	0.305911i	0.999924	+	0.0123500i	$0.00393124\pi$
$311$	0.775655	+	5.39480i	0.0439833	+	0.305911i	−0.955940	+	0.293561i	$0.905160\pi$
$312$	−3.07252	+	1.97459i	−0.173947	+	0.111789i
$313$	−20.0600	+	23.1505i	−1.13386	+	1.30854i	−0.188659	+	0.982043i	$0.560414\pi$
$313$	−20.0600	+	23.1505i	−1.13386	+	1.30854i	−0.945198	+	0.326498i	$0.894131\pi$
$314$	20.2394	−	44.3182i	1.14218	−	2.50102i
$315$	4.69778	+	3.01908i	0.264690	+	0.170106i
$316$	−6.24992	+	1.83514i	−0.351585	+	0.103235i
$317$	−0.468539	−	0.540723i	−0.0263158	−	0.0303700i	0.742439	−	0.669914i	$-0.233669\pi$
$317$	−0.468539	−	0.540723i	−0.0263158	−	0.0303700i	−0.768755	+	0.639544i	$0.779123\pi$
$318$	−4.43080	−	1.30100i	−0.248467	−	0.0729566i
$319$	0.0419048	+	0.0917586i	0.00234622	+	0.00513750i
$320$	−1.94066	+	13.4976i	−0.108486	+	0.754536i
$321$	13.7896			0.769659
$322$	−14.7310	−	7.64817i	−0.820926	−	0.426216i
$323$	−21.5554			−1.19938
$324$	−0.614354	+	4.27292i	−0.0341308	+	0.237385i
$325$	−2.98215	−	6.52999i	−0.165420	−	0.362219i
$326$	56.5685	+	16.6100i	3.13304	+	0.919943i
$327$	−5.34591	−	6.16951i	−0.295630	−	0.341175i
$328$	55.9898	−	16.4401i	3.09152	−	0.907752i
$329$	−10.4067	−	6.68799i	−0.573741	−	0.368721i
$330$	−0.115605	+	0.253140i	−0.00636386	+	0.0139349i
$331$	−18.3506	+	21.1777i	−1.00864	+	1.16403i	−0.0222271	+	0.999753i	$0.507076\pi$
$331$	−18.3506	+	21.1777i	−1.00864	+	1.16403i	−0.986414	+	0.164281i	$0.947470\pi$
$332$	−31.1151	+	19.9965i	−1.70767	+	1.09745i
$333$	0.313382	+	2.17962i	0.0171732	+	0.119442i
$334$	−7.42645	−	51.6521i	−0.406357	−	2.82628i
$335$	−15.1106	+	9.71102i	−0.825582	+	0.530570i
$336$	−5.41201	+	6.24579i	−0.295249	+	0.340736i
$337$	−7.81892	+	17.1210i	−0.425924	+	0.932643i	0.568047	+	0.822996i	$0.307699\pi$
$337$	−7.81892	+	17.1210i	−0.425924	+	0.932643i	−0.993971	+	0.109647i	$0.965028\pi$
$338$	26.6548	+	17.1300i	1.44983	+	0.931750i
$339$	−14.0321	+	4.12018i	−0.762116	+	0.223778i
$340$	−49.4070	−	57.0187i	−2.67947	−	3.09228i
$341$	0.0126355	+	0.00371012i	0.000684251	+	0.000200914i
$342$	−5.22204	−	11.4347i	−0.282376	−	0.618317i
$343$	−2.37200	+	16.4976i	−0.128076	+	0.890789i
$344$	19.1019			1.02990
$345$	19.0864	+	3.73568i	1.02757	+	0.201122i
$346$	9.01004			0.484383
$347$	−2.03201	+	14.1329i	−0.109084	+	0.758696i	0.859702	+	0.510796i	$0.170649\pi$
$347$	−2.03201	+	14.1329i	−0.109084	+	0.758696i	−0.968786	+	0.247900i	$0.920260\pi$
$348$	−6.62535	−	14.5075i	−0.355156	−	0.777683i
$349$	4.50865	+	1.32386i	0.241343	+	0.0708646i	0.400167	−	0.916442i	$-0.368952\pi$
$349$	4.50865	+	1.32386i	0.241343	+	0.0708646i	−0.158824	+	0.987307i	$0.550770\pi$
$350$	−25.9402	−	29.9366i	−1.38656	−	1.60018i
$351$	−0.601808	+	0.176707i	−0.0321221	+	0.00943191i
$352$	−0.0789661	−	0.0507484i	−0.00420891	−	0.00270490i
$353$	7.42472	−	16.2579i	0.395178	−	0.865320i	−0.602558	−	0.798075i	$-0.705852\pi$
$353$	7.42472	−	16.2579i	0.395178	−	0.865320i	0.997737	−	0.0672447i	$-0.0214208\pi$
$354$	6.87912	−	7.93892i	0.365621	−	0.421949i
$355$	24.6506	−	15.8420i	1.30832	−	0.840805i
$356$	−8.18923	−	56.9574i	−0.434028	−	3.01873i
$357$	0.844584	+	5.87421i	0.0447001	+	0.310896i
$358$	43.6956	−	28.0814i	2.30938	−	1.48415i
$359$	22.9288	−	26.4612i	1.21013	−	1.39657i	0.316008	−	0.948757i	$-0.397657\pi$
$359$	22.9288	−	26.4612i	1.21013	−	1.39657i	0.894127	−	0.447814i	$-0.147797\pi$
$360$	9.80970	−	21.4802i	0.517016	−	1.13211i
$361$	5.06084	+	3.25240i	0.266360	+	0.171179i
$362$	−62.4699	+	18.3428i	−3.28334	+	0.964076i
$363$	−7.20298	−	8.31268i	−0.378058	−	0.436303i
$364$	−3.57742	−	1.05042i	−0.187508	−	0.0550572i
$365$	−10.0593	−	22.0269i	−0.526529	−	1.15294i
$366$	−1.65364	+	11.5013i	−0.0864370	+	0.601183i
$367$	14.8756			0.776498			0.388249	−	0.921554i	$-0.373080\pi$
$367$	14.8756			0.776498			0.388249	+	0.921554i	$0.373080\pi$
$368$	−9.49221	+	27.1723i	−0.494816	+	1.41645i
$369$	10.0211			0.521678
$370$	3.19409	−	22.2154i	0.166053	−	1.15492i
$371$	−1.05103	−	2.30144i	−0.0545668	−	0.119485i
$372$	−1.99773	−	0.586588i	−0.103578	−	0.0304132i
$373$	11.4264	+	13.1868i	0.591636	+	0.682785i	0.970065	−	0.242846i	$-0.0780809\pi$
$373$	11.4264	+	13.1868i	0.591636	+	0.682785i	−0.378429	+	0.925630i	$0.623535\pi$
$374$	−0.283769	+	0.0833220i	−0.0146733	+	0.00430848i
$375$	21.9887	+	14.1313i	1.13549	+	0.729735i
$376$	−21.7308	+	47.5839i	−1.12068	+	2.45395i
$377$	1.51748	−	1.75127i	0.0781543	−	0.0901948i
$378$	−2.91153	+	1.87113i	−0.149753	+	0.0962403i
$379$	1.67590	+	11.6561i	0.0860852	+	0.598736i	0.986507	+	0.163718i	$0.0523487\pi$
$379$	1.67590	+	11.6561i	0.0860852	+	0.598736i	−0.900422	+	0.435018i	$0.856742\pi$
$380$	12.4609	+	86.6672i	0.639229	+	4.44593i
$381$	−1.52765	+	0.981759i	−0.0782637	+	0.0502970i
$382$	−13.6438	+	15.7458i	−0.698077	+	0.805624i
$383$	1.19882	−	2.62505i	0.0612568	−	0.134134i	−0.876528	−	0.481351i	$-0.840146\pi$
$383$	1.19882	−	2.62505i	0.0612568	−	0.134134i	0.937785	+	0.347217i	$0.112873\pi$
$384$	−12.8940	−	8.28647i	−0.657994	−	0.422867i
$385$	−0.146295	+	0.0429562i	−0.00745590	+	0.00218925i
$386$	−27.9246	−	32.2267i	−1.42132	−	1.64030i
$387$	3.14751	+	0.924191i	0.159997	+	0.0469793i
$388$	3.88215	+	8.50072i	0.197086	+	0.431559i
$389$	0.649215	−	4.51539i	0.0329165	−	0.228939i	−0.966722	−	0.255830i	$-0.917651\pi$
$389$	0.649215	−	4.51539i	0.0329165	−	0.228939i	0.999638	+	0.0268904i	$0.00856050\pi$
$390$	6.39277			0.323710
$391$	10.2827	+	17.9293i	0.520019	+	0.906725i
$392$	29.7197			1.50107
$393$	0.844727	−	5.87521i	0.0426108	−	0.296365i
$394$	14.1760	+	31.0410i	0.714175	+	1.56382i
$395$	5.87122	+	1.72395i	0.295413	+	0.0867411i
$396$	−0.0771863	−	0.0890777i	−0.00387876	−	0.00447632i
$397$	−4.25519	+	1.24944i	−0.213562	+	0.0627074i	−0.386763	−	0.922179i	$-0.626407\pi$
$397$	−4.25519	+	1.24944i	−0.213562	+	0.0627074i	0.173202	+	0.984886i	$0.444589\pi$
$398$	27.1447	+	17.4448i	1.36064	+	0.874431i
$399$	2.86110	−	6.26494i	0.143234	−	0.313639i
$400$	−44.9827	+	51.9128i	−2.24914	+	2.59564i
$401$	4.63189	−	2.97674i	0.231306	−	0.148651i	−0.419855	−	0.907591i	$-0.637919\pi$
$401$	4.63189	−	2.97674i	0.231306	−	0.148651i	0.651160	+	0.758940i	$0.274283\pi$
$402$	−1.58429	−	11.0190i	−0.0790172	−	0.549577i
$403$	−0.0430521	−	0.299434i	−0.00214458	−	0.0149159i
$404$	48.4796	−	31.1560i	2.41195	−	1.55007i
$405$	2.65565	−	3.06479i	0.131960	−	0.152290i
$406$	5.31172	−	11.6310i	0.263616	−	0.577239i
$407$	−0.0505794	−	0.0325054i	−0.00250713	−	0.00161123i
$408$	24.0792	−	7.07029i	1.19210	−	0.350032i
$409$	−20.4190	−	23.5648i	−1.00966	−	1.16521i	−0.986213	−	0.165480i	$-0.947083\pi$
$409$	−20.4190	−	23.5648i	−1.00966	−	1.16521i	−0.0234433	−	0.999725i	$-0.507463\pi$
$410$	−98.0011	−	28.7757i	−4.83993	−	1.42113i
$411$	−3.34568	−	7.32602i	−0.165030	−	0.361366i
$412$	−5.80697	+	40.3884i	−0.286089	+	1.98979i
$413$	5.75541			0.283205
$414$	−7.02001	+	9.79833i	−0.345015	+	0.481562i
$415$	34.7455			1.70559
$416$	−0.306872	+	2.13434i	−0.0150456	+	0.104645i
$417$	3.19044	+	6.98608i	0.156236	+	0.342110i
$418$	0.329324	+	0.0966981i	0.0161077	+	0.00472966i
$419$	−25.3369	−	29.2403i	−1.23779	−	1.42848i	−0.865908	−	0.500203i	$-0.833259\pi$
$419$	−25.3369	−	29.2403i	−1.23779	−	1.42848i	−0.371880	−	0.928281i	$-0.621287\pi$
$420$	23.1300	−	6.79158i	1.12863	−	0.331395i
$421$	5.63619	+	3.62216i	0.274691	+	0.176533i	0.670732	−	0.741699i	$-0.265980\pi$
$421$	5.63619	+	3.62216i	0.274691	+	0.176533i	−0.396041	+	0.918233i	$0.629616\pi$
$422$	1.40736	−	3.08170i	0.0685094	−	0.150015i
$423$	−5.88291	+	6.78924i	−0.286037	+	0.330104i
$424$	−9.00053	+	5.78429i	−0.437104	+	0.280910i
$425$	7.01989	+	48.8244i	0.340515	+	2.36833i
$426$	2.58452	+	17.9757i	0.125220	+	0.870925i
$427$	−5.35562	+	3.44185i	−0.259177	+	0.166563i
$428$	38.9823	−	44.9880i	1.88428	−	2.17458i
$429$	0.00711412	−	0.0155777i	0.000343473	−	0.000752101i
$430$	−28.1271	−	18.0762i	−1.35641	−	0.871711i
$431$	−4.72227	+	1.38658i	−0.227464	+	0.0667894i	−0.393478	−	0.919334i	$-0.628728\pi$
$431$	−4.72227	+	1.38658i	−0.227464	+	0.0667894i	0.166015	+	0.986123i	$0.446910\pi$
$432$	3.93020	+	4.53569i	0.189092	+	0.218224i
$433$	24.8366	+	7.29268i	1.19357	+	0.350464i	0.817391	−	0.576083i	$-0.195420\pi$
$433$	24.8366	+	7.29268i	1.19357	+	0.350464i	0.376179	+	0.926547i	$0.377238\pi$
$434$	−0.693432	−	1.51841i	−0.0332858	−	0.0728858i
$435$	−2.13221	+	14.8299i	−0.102232	+	0.711038i
$436$	−35.2404			−1.68771
$437$	1.21038	−	23.9562i	0.0579005	−	1.14598i
$438$	15.0077			0.717098
$439$	−0.315656	+	2.19544i	−0.0150655	+	0.104783i	−0.995967	−	0.0897241i	$-0.971401\pi$
$439$	−0.315656	+	2.19544i	−0.0150655	+	0.104783i	0.980901	+	0.194507i	$0.0623106\pi$
$440$	0.267842	+	0.586492i	0.0127689	+	0.0279599i
$441$	4.89705	+	1.43790i	0.233193	+	0.0684716i
$442$	4.44903	+	5.13445i	0.211619	+	0.244221i
$443$	−7.47429	+	2.19465i	−0.355114	+	0.104271i	−0.454424	−	0.890786i	$-0.650155\pi$
$443$	−7.47429	+	2.19465i	−0.355114	+	0.104271i	0.0993095	+	0.995057i	$0.468337\pi$
$444$	7.99685	+	5.13926i	0.379514	+	0.243899i
$445$	−22.4558	+	49.1714i	−1.06451	+	2.33095i
$446$	−38.3947	+	44.3098i	−1.81804	+	2.09813i
$447$	2.43481	−	1.56476i	0.115163	−	0.0740106i
$448$	−0.658976	−	4.58328i	−0.0311337	−	0.216540i
$449$	1.01858	+	7.08436i	0.0480697	+	0.334332i	0.999638	+	0.0268953i	$0.00856207\pi$
$449$	1.01858	+	7.08436i	0.0480697	+	0.334332i	−0.951569	+	0.307437i	$0.900529\pi$
$450$	−24.1996	+	15.5522i	−1.14078	+	0.733135i
$451$	−0.179179	+	0.206784i	−0.00843722	+	0.00973707i
$452$	−26.2259	+	57.4266i	−1.23356	+	2.70112i
$453$	−1.73780	−	1.11682i	−0.0816490	−	0.0524726i
$454$	14.7510	−	4.33127i	0.692297	−	0.203277i
$455$	2.29367	+	2.64703i	0.107529	+	0.124095i
$456$	−27.9448	−	8.20532i	−1.30863	−	0.384249i
$457$	−1.85262	−	4.05667i	−0.0866618	−	0.189763i	0.861339	−	0.508030i	$-0.169626\pi$
$457$	−1.85262	−	4.05667i	−0.0866618	−	0.189763i	−0.948001	+	0.318268i	$0.896899\pi$
$458$	4.92165	−	34.2309i	0.229974	−	1.59950i
$459$	4.30972			0.201161
$460$	66.1436	−	51.7081i	3.08396	−	2.41090i
$461$	−24.0540			−1.12031			−0.560153	−	0.828389i	$-0.689258\pi$
$461$	−24.0540			−1.12031			−0.560153	+	0.828389i	$0.689258\pi$
$462$	0.0134483	−	0.0935349i	0.000625671	−	0.00435164i
$463$	−1.36569	−	2.99043i	−0.0634688	−	0.138977i	0.875240	−	0.483690i	$-0.160704\pi$
$463$	−1.36569	−	2.99043i	−0.0634688	−	0.138977i	−0.938708	+	0.344712i	$0.887976\pi$
$464$	−21.2748	−	6.24685i	−0.987659	−	0.290003i
$465$	1.28085	+	1.47818i	0.0593981	+	0.0685490i
$466$	34.1571	−	10.0294i	1.58230	−	0.464604i
$467$	11.5767	+	7.43992i	0.535708	+	0.344278i	0.780358	−	0.625333i	$-0.215037\pi$
$467$	11.5767	+	7.43992i	0.535708	+	0.344278i	−0.244650	+	0.969611i	$0.578673\pi$
$468$	−1.12478	+	2.46292i	−0.0519928	+	0.113848i
$469$	3.99417	−	4.60951i	0.184434	−	0.212848i
$470$	77.0270	−	49.5023i	3.55299	−	2.28337i
$471$	−2.75877	−	19.1877i	−0.127117	−	0.884121i
$472$	−3.46365	−	24.0902i	−0.159428	−	1.10884i
$473$	−0.0753485	+	0.0484235i	−0.00346453	+	0.00222652i
$474$	−2.48350	+	2.86611i	−0.114071	+	0.131645i
$475$	23.7805	−	52.0720i	1.09112	−	2.38923i
$476$	21.5520	+	13.8506i	0.987835	+	0.634843i
$477$	−1.76292	+	0.517639i	−0.0807184	+	0.0237011i
$478$	33.4724	+	38.6292i	1.53099	+	1.76686i
$479$	22.1960	+	6.51733i	1.01416	+	0.297784i	0.746255	−	0.665661i	$-0.231850\pi$
$479$	22.1960	+	6.51733i	1.01416	+	0.297784i	0.267906	+	0.963445i	$0.413668\pi$
$480$	−5.79156	−	12.6817i	−0.264347	−	0.578840i
$481$	−0.196558	+	1.36709i	−0.00896226	+	0.0623339i
$482$	−19.6238			−0.893841
$483$	−6.57588	+	0.608801i	−0.299213	+	0.0277014i
$484$	−47.4823			−2.15829
$485$	1.24938	−	8.68962i	0.0567313	−	0.394575i
$486$	1.04408	+	2.28621i	0.0473603	+	0.103705i
$487$	−11.1600	−	3.27689i	−0.505710	−	0.148490i	0.0189187	−	0.999821i	$-0.493978\pi$
$487$	−11.1600	−	3.27689i	−0.505710	−	0.148490i	−0.524629	+	0.851331i	$0.675796\pi$
$488$	17.6295	+	20.3455i	0.798049	+	0.920998i
$489$	22.5073	−	6.60874i	1.01782	−	0.298858i
$490$	−43.7615	−	28.1238i	−1.97694	−	1.27050i
$491$	−12.6159	+	27.6249i	−0.569346	+	1.24669i	0.377799	+	0.925888i	$0.376681\pi$
$491$	−12.6159	+	27.6249i	−0.569346	+	1.24669i	−0.947145	+	0.320806i	$0.896046\pi$
$492$	28.3291	−	32.6936i	1.27718	−	1.47394i
$493$	−13.3947	+	8.60828i	−0.603269	+	0.387697i
$494$	−1.12208	−	7.80425i	−0.0504848	−	0.351130i
$495$	0.0157578	+	0.109598i	0.000708260	+	0.00492606i
$496$	−2.43512	+	1.56496i	−0.109340	+	0.0702686i
$497$	−6.51584	+	7.51968i	−0.292276	+	0.337304i
$498$	−8.94560	+	19.5881i	−0.400862	+	0.877765i
$499$	−29.3390	−	18.8551i	−1.31340	−	0.844068i	−0.318793	−	0.947824i	$-0.603277\pi$
$499$	−29.3390	−	18.8551i	−1.31340	−	0.844068i	−0.994603	+	0.103756i	$0.966914\pi$
$500$	108.264	−	31.7890i	4.84169	−	1.42165i
$501$	−13.5966	−	15.6913i	−0.607450	−	0.701035i
$502$	35.9966	+	10.5696i	1.60661	+	0.471743i
$503$	4.66816	+	10.2218i	0.208143	+	0.455770i	0.984696	−	0.174283i	$-0.0557607\pi$
$503$	4.66816	+	10.2218i	0.208143	+	0.455770i	−0.776553	+	0.630052i	$0.783033\pi$
$504$	−1.14116	+	7.93691i	−0.0508311	+	0.353538i
$505$	−54.1360			−2.40902
$506$	−0.0766679	−	0.320053i	−0.00340830	−	0.0142281i
$507$	12.6066			0.559879
$508$	−1.11562	+	7.75927i	−0.0494974	+	0.344262i
$509$	1.81739	+	3.97954i	0.0805546	+	0.176390i	0.945624	−	0.325263i	$-0.105453\pi$
$509$	1.81739	+	3.97954i	0.0805546	+	0.176390i	−0.865069	+	0.501653i	$0.832726\pi$
$510$	−42.1467	−	12.3754i	−1.86629	−	0.547992i
$511$	5.38465	+	6.21421i	0.238203	+	0.274901i
$512$	−47.2669	+	13.8788i	−2.08892	+	0.613363i
$513$	−4.20760	−	2.70406i	−0.185770	−	0.119387i
$514$	−14.2378	+	31.1764i	−0.628001	+	1.37513i
$515$	25.1017	−	28.9689i	1.10611	−	1.27652i
$516$	11.9130	−	7.65600i	0.524439	−	0.337037i
$517$	−0.0349073	−	0.242786i	−0.00153522	−	0.0106777i
$518$	1.08460	+	7.54354i	0.0476544	+	0.331444i
$519$	3.01580	−	1.93814i	0.132379	−	0.0850748i
$520$	9.69925	−	11.1935i	0.425340	−	0.490869i
$521$	−1.29520	+	2.83608i	−0.0567436	+	0.124251i	−0.935880	−	0.352319i	$-0.885393\pi$
$521$	−1.29520	+	2.83608i	−0.0567436	+	0.124251i	0.879136	+	0.476571i	$0.158120\pi$
$522$	−7.81153	−	5.02016i	−0.341901	−	0.219727i
$523$	−12.4643	+	3.65986i	−0.545027	+	0.160034i	−0.542644	−	0.839963i	$-0.682577\pi$
$523$	−12.4643	+	3.65986i	−0.545027	+	0.160034i	−0.00238288	+	0.999997i	$0.500758\pi$
$524$	−16.7797	−	19.3648i	−0.733023	−	0.845954i
$525$	−15.1222	−	4.44029i	−0.659989	−	0.193790i
$526$	−7.42845	−	16.2660i	−0.323896	−	0.709233i
$527$	−0.295820	+	2.05747i	−0.0128861	+	0.0896249i
$528$	−0.163866			−0.00713135
$529$	−20.5036	+	10.4212i	−0.891462	+	0.453096i
$530$	18.7268			0.813439
$531$	0.594817	−	4.13704i	0.0258128	−	0.179532i
$532$	−12.3510	−	27.0449i	−0.535483	−	1.17254i
$533$	6.03079	+	1.77080i	0.261222	+	0.0767018i
$534$	−21.9394	−	25.3194i	−0.949410	−	1.09568i
$535$	−53.6555	+	15.7547i	−2.31973	+	0.681135i
$536$	−21.6976	−	13.9442i	−0.937194	−	0.602298i
$537$	8.58503	−	18.7986i	0.370471	−	0.811219i
$538$	−23.4212	+	27.0295i	−1.00976	+	1.16532i
$539$	−0.117231	+	0.0753398i	−0.00504949	+	0.00324511i
$540$	−2.49138	−	17.3280i	−0.107212	−	0.745677i
$541$	4.61797	+	32.1187i	0.198542	+	1.38089i	0.808518	+	0.588471i	$0.200270\pi$
$541$	4.61797	+	32.1187i	0.198542	+	1.38089i	−0.609976	+	0.792420i	$0.708821\pi$
$542$	−17.1756	+	11.0381i	−0.737754	+	0.474126i
$543$	−16.9639	+	19.5774i	−0.727993	+	0.840148i
$544$	6.15492	−	13.4774i	0.263890	−	0.577839i
$545$	27.8498	+	17.8980i	1.19295	+	0.766665i
$546$	−2.08282	+	0.611572i	−0.0891365	+	0.0261728i
$547$	5.89308	+	6.80097i	0.251970	+	0.290789i	0.867617	−	0.497233i	$-0.165651\pi$
$547$	5.89308	+	6.80097i	0.251970	+	0.290789i	−0.615647	+	0.788022i	$0.711105\pi$
$548$	−33.3590	−	9.79507i	−1.42502	−	0.418425i
$549$	1.92053	+	4.20538i	0.0819663	+	0.179481i
$550$	0.111778	−	0.777430i	0.00476621	−	0.0331497i
$551$	18.4785			0.787209
$552$	6.50566	+	27.1581i	0.276899	+	1.15592i
$553$	−2.07782			−0.0883579
$554$	−1.32789	+	9.23567i	−0.0564166	+	0.392386i
$555$	−3.70961	−	8.12291i	−0.157464	−	0.344798i
$556$	31.8110	+	9.34056i	1.34909	+	0.396128i
$557$	20.6639	+	23.8474i	0.875556	+	1.01045i	0.999834	+	0.0181980i	$0.00579291\pi$
$557$	20.6639	+	23.8474i	0.875556	+	1.01045i	−0.124279	+	0.992247i	$0.539662\pi$
$558$	−1.16311	+	0.341519i	−0.0492383	+	0.0144577i
$559$	1.73088	+	1.11237i	0.0732086	+	0.0470483i
$560$	13.9224	−	30.4858i	0.588328	−	1.28826i
$561$	−0.0770586	+	0.0889303i	−0.00325342	+	0.00375464i
$562$	−26.4838	+	17.0201i	−1.11715	+	0.717951i
$563$	−5.12498	−	35.6450i	−0.215992	−	1.50226i	−0.752628	−	0.658446i	$-0.771214\pi$
$563$	−5.12498	−	35.6450i	−0.215992	−	1.50226i	0.536636	−	0.843814i	$-0.319695\pi$
$564$	5.51902	+	38.3856i	0.232393	+	1.61633i
$565$	49.8917	−	32.0635i	2.09896	−	1.34892i
$566$	−40.2487	+	46.4495i	−1.69178	+	1.95242i
$567$	−0.572039	+	1.25259i	−0.0240234	+	0.0526039i
$568$	35.3962	+	22.7477i	1.48519	+	0.954474i
$569$	−31.2963	+	9.18942i	−1.31201	+	0.385241i	−0.861603	−	0.507583i	$-0.830539\pi$
$569$	−31.2963	+	9.18942i	−1.31201	+	0.385241i	−0.450406	+	0.892824i	$0.648721\pi$
$570$	33.3833	+	38.5264i	1.39827	+	1.61369i
$571$	32.7363	+	9.61224i	1.36997	+	0.402260i	0.882267	−	0.470749i	$-0.156016\pi$
$571$	32.7363	+	9.61224i	1.36997	+	0.402260i	0.487704	+	0.873009i	$0.337835\pi$
$572$	−0.0307107	−	0.0672470i	−0.00128408	−	0.00281174i
$573$	−1.17974	+	8.20526i	−0.0492842	+	0.342779i
$574$	34.6825			1.44762
$575$	−54.6565	+	5.06014i	−2.27933	+	0.211022i
$576$	−3.36261			−0.140109
$577$	5.54883	−	38.5929i	0.231001	−	1.60664i	−0.462790	−	0.886468i	$-0.653152\pi$
$577$	5.54883	−	38.5929i	0.231001	−	1.60664i	0.693791	−	0.720177i	$-0.255939\pi$
$578$	−1.64306	−	3.59781i	−0.0683425	−	0.149649i
$579$	−16.2790	−	4.77996i	−0.676534	−	0.198648i
$580$	42.3543	+	48.8795i	1.75867	+	2.02961i
$581$	−11.3204	+	3.32397i	−0.469650	+	0.137902i
$582$	4.57719	+	2.94158i	0.189731	+	0.121933i
$583$	0.0208399	−	0.0456330i	0.000863099	−	0.00188992i
$584$	22.7701	−	26.2781i	0.942233	−	1.08739i
$585$	2.13976	−	1.37514i	0.0884682	−	0.0568551i
$586$	−6.10663	−	42.4726i	−0.252263	−	1.75453i
$587$	−4.67494	−	32.5149i	−0.192955	−	1.34203i	−0.824133	−	0.566396i	$-0.808337\pi$
$587$	−4.67494	−	32.5149i	−0.192955	−	1.34203i	0.631177	−	0.775638i	$-0.282572\pi$
$588$	18.5348	−	11.9116i	0.764362	−	0.491226i
$589$	1.57973	−	1.82311i	0.0650918	−	0.0751200i
$590$	−17.6965	+	38.7500i	−0.728555	+	1.59531i
$591$	11.4221	+	7.34055i	0.469843	+	0.301950i
$592$	12.6804	−	3.72329i	0.521159	−	0.153026i
$593$	0.143737	+	0.165882i	0.00590259	+	0.00681195i	0.758693	−	0.651448i	$-0.225838\pi$
$593$	0.143737	+	0.165882i	0.00590259	+	0.00681195i	−0.752791	+	0.658260i	$0.771293\pi$
$594$	−0.0658439	−	0.0193335i	−0.00270161	−	0.000793263i
$595$	−9.99763	−	21.8918i	−0.409863	−	0.897475i
$596$	1.77810	−	12.3670i	0.0728340	−	0.506572i
$597$	12.8383			0.525436
$598$	−5.95613	+	4.65623i	−0.243564	+	0.190407i
$599$	−3.53619			−0.144485			−0.0722425	−	0.997387i	$-0.523016\pi$
$599$	−3.53619			−0.144485			−0.0722425	+	0.997387i	$0.523016\pi$
$600$	−9.48489	+	65.9689i	−0.387219	+	2.69317i
$601$	15.0669	+	32.9918i	0.614590	+	1.34577i	0.919389	+	0.393348i	$0.128683\pi$
$601$	15.0669	+	32.9918i	0.614590	+	1.34577i	−0.304799	+	0.952417i	$0.598589\pi$
$602$	10.8933	+	3.19857i	0.443979	+	0.130364i
$603$	−2.90057	−	3.34743i	−0.118120	−	0.136318i
$604$	−8.55624	+	2.51234i	−0.348148	+	0.102226i
$605$	37.5243	+	24.1154i	1.52558	+	0.980430i
$606$	13.9379	−	30.5197i	0.566188	−	1.23978i
$607$	29.3523	−	33.8743i	1.19137	−	1.37492i	0.281746	−	0.959489i	$-0.409086\pi$
$607$	29.3523	−	33.8743i	1.19137	−	1.37492i	0.909626	−	0.415428i	$-0.136368\pi$
$608$	−14.4652	+	9.29624i	−0.586643	+	0.377012i
$609$	−0.724023	−	5.03569i	−0.0293389	−	0.204056i
$610$	−6.70598	−	46.6411i	−0.271517	−	1.88844i
$611$	−4.74009	+	3.04627i	−0.191763	+	0.123239i
$612$	12.1833	−	14.0603i	0.492482	−	0.568355i
$613$	0.674111	−	1.47610i	0.0272271	−	0.0596190i	−0.895530	−	0.445001i	$-0.853203\pi$
$613$	0.674111	−	1.47610i	0.0272271	−	0.0596190i	0.922757	+	0.385382i	$0.125930\pi$
$614$	−46.6377	−	29.9722i	−1.88214	−	1.20958i
$615$	−38.9924	+	11.4492i	−1.57233	+	0.461676i
$616$	−0.143373	−	0.165461i	−0.00577665	−	0.00666661i
$617$	18.6179	+	5.46671i	0.749529	+	0.220082i	0.634118	−	0.773236i	$-0.281363\pi$
$617$	18.6179	+	5.46671i	0.749529	+	0.220082i	0.115411	+	0.993318i	$0.463182\pi$
$618$	9.86880	+	21.6097i	0.396981	+	0.869268i
$619$	1.55013	−	10.7814i	0.0623051	−	0.433341i	−0.934663	−	0.355534i	$-0.884299\pi$
$619$	1.55013	−	10.7814i	0.0623051	−	0.433341i	0.996968	−	0.0778073i	$-0.0247919\pi$
$620$	8.44342			0.339096
$621$	−0.242000	+	4.78972i	−0.00971114	+	0.192205i
$622$	13.6984			0.549255
$623$	2.61227	−	18.1688i	0.104658	−	0.727916i
$624$	1.56374	+	3.42411i	0.0625996	+	0.137074i
$625$	−46.7946	−	13.7401i	−1.87178	−	0.549606i
$626$	50.4175	+	58.1849i	2.01509	+	2.32554i
$627$	0.131030	−	0.0384740i	0.00523285	−	0.00153650i
$628$	−70.3980	−	45.2421i	−2.80919	−	1.80535i
$629$	3.94235	−	8.63254i	0.157192	−	0.344202i
$630$	9.19106	−	10.6070i	0.366180	−	0.422595i
$631$	36.6812	−	23.5736i	1.46026	−	0.938449i	0.461575	−	0.887101i	$-0.347285\pi$
$631$	36.6812	−	23.5736i	1.46026	−	0.938449i	0.998681	−	0.0513479i	$-0.0163517\pi$
$632$	1.25045	+	8.69706i	0.0497401	+	0.345950i
$633$	−0.191833	−	1.33423i	−0.00762468	−	0.0530308i
$634$	−1.51278	+	0.972203i	−0.0600800	+	0.0386111i
$635$	4.82244	−	5.56540i	0.191373	−	0.220856i
$636$	−3.29489	+	7.21480i	−0.130651	+	0.286085i
$637$	2.69299	+	1.73068i	0.106700	+	0.0685721i
$638$	0.243262	−	0.0714281i	0.00963082	−	0.00282786i
$639$	4.73181	+	5.46080i	0.187187	+	0.216026i
$640$	59.6382	+	17.5114i	2.35741	+	0.692198i
$641$	−2.92279	−	6.40002i	−0.115443	−	0.252786i	0.843086	−	0.537778i	$-0.180736\pi$
$641$	−2.92279	−	6.40002i	−0.115443	−	0.252786i	−0.958530	+	0.284993i	$0.908009\pi$
$642$	4.93232	−	34.3051i	0.194663	−	1.35391i
$643$	−9.53363			−0.375970			−0.187985	−	0.982172i	$-0.560196\pi$
$643$	−9.53363			−0.375970			−0.187985	+	0.982172i	$0.560196\pi$
$644$	−16.6035	+	23.1747i	−0.654268	+	0.913209i
$645$	−13.3029			−0.523802
$646$	−7.71006	+	53.6246i	−0.303348	+	2.10983i
$647$	−7.37566	−	16.1504i	−0.289967	−	0.634939i	0.707450	−	0.706763i	$-0.249845\pi$
$647$	−7.37566	−	16.1504i	−0.289967	−	0.634939i	−0.997417	+	0.0718238i	$0.977118\pi$
$648$	5.58718	+	1.64055i	0.219485	+	0.0644467i
$649$	0.0747317	+	0.0862450i	0.00293347	+	0.00338541i
$650$	−17.3117	+	5.08317i	−0.679020	+	0.199378i
$651$	−0.558725	−	0.359071i	−0.0218982	−	0.0140731i
$652$	42.0661	−	92.1119i	1.64744	−	3.60738i
$653$	16.0888	−	18.5675i	0.629604	−	0.726602i	−0.347897	−	0.937533i	$-0.613104\pi$
$653$	16.0888	−	18.5675i	0.629604	−	0.726602i	0.977501	+	0.210931i	$0.0676495\pi$
$654$	−17.2604	+	11.0926i	−0.674934	+	0.433754i
$655$	3.42562	+	23.8257i	0.133850	+	0.930946i
$656$	−8.55918	−	59.5304i	−0.334180	−	2.32427i
$657$	5.02333	−	3.22830i	0.195979	−	0.125948i
$658$	−20.3604	+	23.4972i	−0.793731	+	0.916015i
$659$	−0.693556	+	1.51868i	−0.0270171	+	0.0591592i	−0.922659	−	0.385616i	$-0.873989\pi$
$659$	−0.693556	+	1.51868i	−0.0270171	+	0.0591592i	0.895642	+	0.444775i	$0.146716\pi$
$660$	0.402106	+	0.258418i	0.0156519	+	0.0100589i
$661$	−12.6102	+	3.70269i	−0.490480	+	0.144018i	−0.517615	−	0.855614i	$-0.673180\pi$
$661$	−12.6102	+	3.70269i	−0.490480	+	0.144018i	0.0271347	+	0.999632i	$0.491362\pi$
$662$	46.1213	+	53.2268i	1.79255	+	2.06872i
$663$	2.59362	+	0.761557i	0.100728	+	0.0295764i
$664$	20.7257	+	45.3830i	0.804315	+	1.76120i
$665$	−3.97487	+	27.6459i	−0.154139	+	1.07206i
$666$	5.53445			0.214456
$667$	−8.81489	−	15.3700i	−0.341314	−	0.595128i
$668$	−89.6290			−3.46785
$669$	−3.31988	+	23.0902i	−0.128354	+	0.892720i
$670$	18.7538	+	41.0651i	0.724522	+	1.58648i
$671$	−0.121117	−	0.0355631i	−0.00467566	−	0.00137290i
$672$	3.10016	+	3.57777i	0.119591	+	0.138015i
$673$	22.3895	−	6.57416i	0.863053	−	0.253415i	0.179895	−	0.983686i	$-0.442424\pi$
$673$	22.3895	−	6.57416i	0.863053	−	0.253415i	0.683158	+	0.730271i	$0.260606\pi$
$674$	39.7963	+	25.5755i	1.53289	+	0.985131i
$675$	−4.75459	+	10.4111i	−0.183004	+	0.400723i
$676$	35.6382	−	41.1286i	1.37070	−	1.58187i
$677$	−20.2228	+	12.9964i	−0.777224	+	0.499491i	−0.868111	−	0.496370i	$-0.834666\pi$
$677$	−20.2228	+	12.9964i	−0.777224	+	0.499491i	0.0908875	+	0.995861i	$0.471030\pi$
$678$	5.23095	+	36.3820i	0.200893	+	1.39724i
$679$	0.424244	+	2.95068i	0.0162810	+	0.113237i
$680$	−85.6149	+	55.0214i	−3.28318	+	2.10997i
$681$	4.00568	−	4.62280i	0.153498	−	0.177146i
$682$	0.0137494	−	0.0301070i	0.000526491	−	0.00115286i
$683$	−5.04023	−	3.23916i	−0.192859	−	0.123943i	0.440648	−	0.897680i	$-0.354749\pi$
$683$	−5.04023	−	3.23916i	−0.192859	−	0.123943i	−0.633507	+	0.773737i	$0.718385\pi$
$684$	−20.7166	+	6.08293i	−0.792117	+	0.232587i
$685$	21.3882	+	24.6833i	0.817200	+	0.943099i
$686$	40.1936	+	11.8019i	1.53460	+	0.450599i
$687$	−5.71600	−	12.5163i	−0.218079	−	0.477527i
$688$	2.80182	−	19.4871i	0.106819	−	0.742939i
$689$	−1.15241			−0.0439032
$690$	16.1204	−	46.1460i	0.613691	−	1.75675i
$691$	27.1419			1.03253			0.516264	−	0.856430i	$-0.327322\pi$
$691$	27.1419			1.03253			0.516264	+	0.856430i	$0.327322\pi$
$692$	2.20239	−	15.3180i	0.0837223	−	0.582302i
$693$	−0.0156188	−	0.0342005i	−0.000593310	−	0.00129917i
$694$	34.4325	+	10.1103i	1.30704	+	0.383781i
$695$	−20.3957	−	23.5379i	−0.773654	−	0.892844i
$696$	−20.6420	+	6.06103i	−0.782432	+	0.229743i
$697$	−36.3322	−	23.3493i	−1.37618	−	0.884418i
$698$	4.90612	−	10.7429i	0.185699	−	0.406625i
$699$	9.27550	−	10.7045i	0.350831	−	0.404881i
$700$	−57.2360	+	36.7834i	−2.16332	+	1.39028i
$701$	7.12129	+	49.5297i	0.268967	+	1.87071i	0.458301	+	0.888797i	$0.348458\pi$
$701$	7.12129	+	49.5297i	0.268967	+	1.87071i	−0.189334	+	0.981913i	$0.560633\pi$
$702$	0.224345	+	1.56036i	0.00846737	+	0.0588918i
$703$	−9.26527	+	5.95443i	−0.349446	+	0.224576i
$704$	0.0601240	−	0.0693868i	0.00226601	−	0.00261511i
$705$	15.1338	−	33.1384i	0.569972	−	1.24806i
$706$	−37.7899	−	24.2861i	−1.42224	−	0.914019i
$707$	17.6380	−	5.17898i	0.663345	−	0.194776i
$708$	−11.8154	−	13.6358i	−0.444052	−	0.512463i
$709$	−29.6798	−	8.71476i	−1.11465	−	0.327290i	−0.327990	−	0.944681i	$-0.606371\pi$
$709$	−29.6798	−	8.71476i	−1.11465	−	0.327290i	−0.786656	+	0.617391i	$0.788190\pi$
$710$	−30.5938	−	66.9911i	−1.14816	−	2.51413i
$711$	−0.214741	+	1.49355i	−0.00805341	+	0.0560127i
$712$	−77.6204			−2.90895
$713$	−2.27001	−	0.444298i	−0.0850127	−	0.0166391i
$714$	14.9157			0.558206
$715$	−0.00988351	+	0.0687413i	−0.000369622	+	0.00257078i
$716$	−37.0604	−	81.1510i	−1.38501	−	3.03275i
$717$	19.5132	+	5.72960i	0.728735	+	0.213976i
$718$	−57.6278	−	66.5060i	−2.15065	−	2.48198i
$719$	18.1350	−	5.32490i	0.676320	−	0.198585i	0.0745044	−	0.997221i	$-0.476263\pi$
$719$	18.1350	−	5.32490i	0.676320	−	0.198585i	0.601815	+	0.798635i	$0.294444\pi$
$720$	−20.4746	−	13.1582i	−0.763042	−	0.490378i
$721$	−5.40701	+	11.8397i	−0.201368	+	0.440933i
$722$	9.90136	−	11.4268i	0.368491	−	0.425261i
$723$	−6.56840	+	4.22126i	−0.244282	+	0.156990i
$724$	15.9146	+	110.689i	0.591462	+	4.11371i
$725$	−6.01782	−	41.8549i	−0.223496	−	1.55445i
$726$	−23.2563	+	14.9459i	−0.863123	+	0.554695i
$727$	−1.32855	+	1.53323i	−0.0492731	+	0.0568642i	−0.779851	−	0.625965i	$-0.784705\pi$
$727$	−1.32855	+	1.53323i	−0.0492731	+	0.0568642i	0.730578	+	0.682829i	$0.239251\pi$
$728$	−2.08926	+	4.57485i	−0.0774332	+	0.169555i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−58.3955	+	17.1465i	−2.16131	+	0.634619i
$731$	−9.25812	−	10.6844i	−0.342424	−	0.395178i
$732$	19.1491	+	5.62270i	0.707773	+	0.207821i
$733$	16.5986	+	36.3460i	0.613085	+	1.34247i	0.920444	+	0.390875i	$0.127828\pi$
$733$	16.5986	+	36.3460i	0.613085	+	1.34247i	−0.307359	+	0.951594i	$0.599445\pi$
$734$	5.32077	−	37.0068i	0.196393	−	1.36594i
$735$	−20.6974			−0.763433
$736$	14.6328	+	7.59722i	0.539374	+	0.280037i
$737$	0.120936			0.00445474
$738$	3.58440	−	24.9301i	0.131944	−	0.917689i
$739$	0.869793	+	1.90458i	0.0319958	+	0.0700611i	0.924955	−	0.380076i	$-0.124102\pi$
$739$	0.869793	+	1.90458i	0.0319958	+	0.0700611i	−0.892959	+	0.450137i	$0.851375\pi$
$740$	−36.9876	−	10.8605i	−1.35969	−	0.399241i
$741$	−2.05434	−	2.37084i	−0.0754681	−	0.0870948i
$742$	−6.10135	+	1.79152i	−0.223988	+	0.0657687i
$743$	42.2305	+	27.1399i	1.54929	+	0.995666i	0.985486	+	0.169756i	$0.0542979\pi$
$743$	42.2305	+	27.1399i	1.54929	+	0.995666i	0.563801	+	0.825911i	$0.309338\pi$
$744$	−1.16671	+	2.55473i	−0.0427735	+	0.0936609i
$745$	−7.68617	+	8.87031i	−0.281599	+	0.324983i
$746$	36.8925	−	23.7094i	1.35073	−	0.868061i
$747$	1.21935	+	8.48074i	0.0446135	+	0.310294i
$748$	0.0722920	+	0.502802i	0.00264326	+	0.0183843i
$749$	15.9743	−	10.2660i	0.583687	−	0.375113i
$750$	43.0201	−	49.6479i	1.57087	−	1.81288i
$751$	6.50791	−	14.2503i	0.237477	−	0.520002i	−0.752944	−	0.658085i	$-0.771367\pi$
$751$	6.50791	−	14.2503i	0.237477	−	0.520002i	0.990421	+	0.138083i	$0.0440941\pi$
$752$	45.3561	+	29.1486i	1.65397	+	1.06294i
$753$	14.3222	−	4.20539i	0.521932	−	0.153253i
$754$	−3.81394	−	4.40152i	−0.138896	−	0.160294i
$755$	8.03779	+	2.36011i	0.292525	+	0.0858932i
$756$	2.46941	+	5.40726i	0.0898117	+	0.196660i
$757$	4.29183	−	29.8503i	0.155989	−	1.08493i	−0.749942	−	0.661503i	$-0.769919\pi$
$757$	4.29183	−	29.8503i	0.155989	−	1.08493i	0.905931	−	0.423425i	$-0.139172\pi$
$758$	29.5971			1.07501
$759$	−0.0945080	−	0.0906347i	−0.00343042	−	0.00328983i
$760$	118.108			4.28424
$761$	3.59171	−	24.9809i	0.130199	−	0.905555i	−0.815093	−	0.579330i	$-0.803314\pi$
$761$	3.59171	−	24.9809i	0.130199	−	0.905555i	0.945292	−	0.326225i	$-0.105777\pi$
$762$	1.89596	+	4.15157i	0.0686833	+	0.150396i
$763$	−10.7859	−	3.16704i	−0.390477	−	0.114654i
$764$	23.4343	+	27.0447i	0.847824	+	0.978441i
$765$	−16.7692	+	4.92389i	−0.606293	+	0.178024i
$766$	−6.10168	−	3.92131i	−0.220463	−	0.141683i
$767$	1.08901	−	2.38460i	0.0393218	−	0.0861028i
$768$	−20.8226	+	24.0306i	−0.751372	+	0.867129i
$769$	21.5111	−	13.8243i	0.775708	−	0.498517i	−0.0918985	−	0.995768i	$-0.529294\pi$
$769$	21.5111	−	13.8243i	0.775708	−	0.498517i	0.867607	+	0.497251i	$0.165657\pi$
$770$	0.0545368	+	0.379312i	0.00196537	+	0.0136694i
$771$	1.94070	+	13.4979i	0.0698928	+	0.486115i
$772$	−61.6144	+	39.5972i	−2.21755	+	1.42513i
$773$	17.3482	−	20.0209i	0.623971	−	0.720101i	−0.352485	−	0.935818i	$-0.614663\pi$
$773$	17.3482	−	20.0209i	0.623971	−	0.720101i	0.976456	+	0.215716i	$0.0692086\pi$
$774$	3.42498	−	7.49965i	0.123108	−	0.269570i
$775$	−4.64393	−	2.98447i	−0.166815	−	0.107205i
$776$	12.0952	−	3.55148i	0.434194	−	0.127491i
$777$	1.98571	+	2.29163i	0.0712370	+	0.0822119i
$778$	−11.0010	−	3.23017i	−0.394404	−	0.115807i
$779$	20.8212	+	45.5921i	0.745997	+	1.63350i
$780$	1.56263	−	10.8683i	0.0559512	−	0.389149i
$781$	−0.197288			−0.00705952
$782$	48.2817	−	19.1678i	1.72655	−	0.685440i
$783$	−3.69452			−0.132031
$784$	4.35922	−	30.3190i	0.155686	−	1.08282i
$785$	32.6565	+	71.5078i	1.16556	+	2.55222i
$786$	−14.3139	−	4.20295i	−0.510561	−	0.149914i
$787$	11.2996	+	13.0404i	0.402786	+	0.464839i	0.920516	−	0.390704i	$-0.127768\pi$
$787$	11.2996	+	13.0404i	0.402786	+	0.464839i	−0.517731	+	0.855544i	$0.673223\pi$
$788$	56.2380	−	16.5130i	2.00340	−	0.588250i
$789$	−5.98538	−	3.84657i	−0.213085	−	0.136942i
$790$	6.38880	−	13.9895i	0.227303	−	0.497725i
$791$	−13.1878	+	15.2195i	−0.468904	+	0.541144i
$792$	−0.133752	+	0.0859573i	−0.00475268	+	0.00305436i
$793$	0.412673	+	2.87020i	0.0146544	+	0.101924i
$794$	1.58627	+	11.0328i	0.0562947	+	0.391538i
$795$	6.26815	−	4.02829i	0.222308	−	0.142869i
$796$	36.2931	−	41.8845i	1.28638	−	1.48456i
$797$	−13.3136	+	29.1526i	−0.471590	+	1.03264i	0.513101	+	0.858328i	$0.328497\pi$
$797$	−13.3136	+	29.1526i	−0.471590	+	1.03264i	−0.984691	+	0.174310i	$0.944231\pi$
$798$	−14.5623	−	9.35859i	−0.515498	−	0.331291i
$799$	37.1479	−	10.9076i	1.31420	−	0.385883i
$800$	25.7674	+	29.7372i	0.911016	+	1.05137i
$801$	−12.7899	−	3.75545i	−0.451908	−	0.132692i
$802$	−5.74863	−	12.5877i	−0.202991	−	0.444489i
$803$	−0.0232027	+	0.161378i	−0.000818804	+	0.00569491i
$804$	−19.1206			−0.674332
$805$	24.8914	−	9.88186i	0.877305	−	0.348290i
$806$	−0.760317			−0.0267810
$807$	−2.02516	+	14.0853i	−0.0712890	+	0.495826i
$808$	−32.2922	−	70.7100i	−1.13604	−	2.48757i
$809$	−12.0192	−	3.52914i	−0.422571	−	0.124078i	0.0635315	−	0.997980i	$-0.479764\pi$
$809$	−12.0192	−	3.52914i	−0.422571	−	0.124078i	−0.486102	+	0.873902i	$0.661582\pi$
$810$	−6.67455	−	7.70284i	−0.234520	−	0.270650i
$811$	−7.39961	+	2.17272i	−0.259836	+	0.0762946i	−0.409056	−	0.912509i	$-0.634142\pi$
$811$	−7.39961	+	2.17272i	−0.259836	+	0.0762946i	0.149220	+	0.988804i	$0.452324\pi$
$812$	−18.4755	−	11.8735i	−0.648364	−	0.416678i
$813$	−3.37455	+	7.38923i	−0.118351	+	0.259152i
$814$	−0.0989570	+	0.114202i	−0.00346844	+	0.00400279i
$815$	−80.0260	+	51.4296i	−2.80319	+	1.80150i
$816$	−3.68099	−	25.6019i	−0.128861	−	0.896245i
$817$	2.33498	+	16.2401i	0.0816905	+	0.568170i
$818$	−65.9271	+	42.3688i	−2.30509	+	1.48139i
$819$	−0.565599	+	0.652736i	−0.0197636	+	0.0228084i
$820$	−72.8767	+	159.578i	−2.54496	+	5.57270i
$821$	−27.6782	−	17.7877i	−0.965977	−	0.620796i	−0.0403314	−	0.999186i	$-0.512841\pi$
$821$	−27.6782	−	17.7877i	−0.965977	−	0.620796i	−0.925646	+	0.378390i	$0.876478\pi$
$822$	−19.4220	+	5.70283i	−0.677422	+	0.198909i
$823$	−18.7991	−	21.6953i	−0.655295	−	0.756251i	0.326706	−	0.945126i	$-0.394061\pi$
$823$	−18.7991	−	21.6953i	−0.655295	−	0.756251i	−0.982001	+	0.188875i	$0.939516\pi$
$824$	52.8110	+	15.5067i	1.83976	+	0.540202i
$825$	−0.129818	−	0.284262i	−0.00451969	−	0.00989675i
$826$	2.05863	−	14.3181i	0.0716288	−	0.498189i
$827$	−10.6363			−0.369861			−0.184931	−	0.982752i	$-0.559206\pi$
$827$	−10.6363			−0.369861			−0.184931	+	0.982752i	$0.559206\pi$
$828$	14.9422	+	14.3298i	0.519277	+	0.497995i
$829$	−22.6856			−0.787903			−0.393952	−	0.919131i	$-0.628892\pi$
$829$	−22.6856			−0.787903			−0.393952	+	0.919131i	$0.628892\pi$
$830$	12.4280	−	86.4383i	0.431381	−	3.00032i
$831$	1.54221	+	3.37697i	0.0534986	+	0.117146i
$832$	−2.02364	−	0.594195i	−0.0701572	−	0.0206000i
$833$	−14.4043	−	16.6234i	−0.499078	−	0.575966i
$834$	18.5208	−	5.43820i	0.641324	−	0.188310i
$835$	70.8320	+	45.5210i	2.45124	+	1.57532i
$836$	0.244895	−	0.536246i	0.00846989	−	0.0185465i
$837$	−0.315847	+	0.364507i	−0.0109173	+	0.0125992i
$838$	−81.8054	+	52.5731i	−2.82592	+	1.81611i
$839$	−1.65201	−	11.4900i	−0.0570337	−	0.396678i	−0.998263	−	0.0589104i	$-0.981237\pi$
$839$	−1.65201	−	11.4900i	−0.0570337	−	0.396678i	0.941230	−	0.337767i	$-0.109672\pi$
$840$	−4.62772	−	32.1865i	−0.159672	−	1.11054i
$841$	−12.9137	+	8.29911i	−0.445299	+	0.286176i
$842$	11.0270	−	12.7259i	0.380016	−	0.438562i
$843$	−5.20338	+	11.3938i	−0.179214	+	0.392424i
$844$	−4.89518	−	3.14594i	−0.168499	−	0.108288i
$845$	−49.0526	+	14.4031i	−1.68746	+	0.495483i
$846$	14.7857	+	17.0637i	0.508344	+	0.586660i
$847$	−14.5328	−	4.26721i	−0.499352	−	0.146623i
$848$	4.58077	+	10.0305i	0.157304	+	0.344448i
$849$	−3.48019	+	24.2052i	−0.119440	+	0.830721i
$850$	123.974			4.25228
$851$	9.37263	+	4.86617i	0.321290	+	0.166810i
$852$	31.1922			1.06863
$853$	2.17228	−	15.1086i	0.0743776	−	0.517307i	−0.918240	−	0.396024i	$-0.870390\pi$
$853$	2.17228	−	15.1086i	0.0743776	−	0.517307i	0.992618	−	0.121284i	$-0.0387011\pi$
$854$	6.64685	+	14.5546i	0.227450	+	0.498047i
$855$	19.4613	+	5.71435i	0.665562	+	0.195427i
$856$	−52.5836	−	60.6848i	−1.79727	−	2.07416i
$857$	−26.1726	+	7.68498i	−0.894040	+	0.262514i	−0.696309	−	0.717742i	$-0.745176\pi$
$857$	−26.1726	+	7.68498i	−0.894040	+	0.262514i	−0.197731	+	0.980256i	$0.563357\pi$
$858$	−0.0362090	−	0.0232701i	−0.00123615	−	0.000794428i
$859$	5.19844	−	11.3830i	0.177368	−	0.388383i	−0.799978	−	0.600030i	$-0.795155\pi$
$859$	5.19844	−	11.3830i	0.177368	−	0.388383i	0.977346	+	0.211647i	$0.0678827\pi$
$860$	−37.6066	+	43.4003i	−1.28237	+	1.47994i
$861$	11.6088	−	7.46051i	0.395626	−	0.254253i
$862$	1.76039	+	12.2438i	0.0599593	+	0.417026i
$863$	2.92036	+	20.3116i	0.0994102	+	0.691413i	0.977193	+	0.212354i	$0.0681130\pi$
$863$	2.92036	+	20.3116i	0.0994102	+	0.691413i	−0.877783	+	0.479059i	$0.840978\pi$
$864$	2.89213	−	1.85866i	0.0983923	−	0.0632329i
$865$	−9.52022	+	10.9869i	−0.323697	+	0.373567i
$866$	27.0261	−	59.1789i	0.918384	−	2.01098i
$867$	−1.32388	−	0.850806i	−0.0449613	−	0.0288949i
$868$	−2.75094	+	0.807749i	−0.0933730	+	0.0274168i
$869$	−0.0269796	−	0.0311362i	−0.000915221	−	0.00105622i
$870$	36.1304	+	10.6089i	1.22494	+	0.359674i
$871$	−1.15407	−	2.52706i	−0.0391042	−	0.0856262i
$872$	−6.76510	+	47.0523i	−0.229095	+	1.59339i
$873$	2.16482			0.0732680
$874$	−59.1642	−	11.5799i	−2.00126	−	0.391696i
$875$	35.9928			1.21678
$876$	3.66845	−	25.5147i	0.123946	−	0.862061i
$877$	−19.8073	−	43.3720i	−0.668846	−	1.46457i	−0.874043	−	0.485849i	$-0.838511\pi$
$877$	−19.8073	−	43.3720i	−0.668846	−	1.46457i	0.205197	−	0.978721i	$-0.434217\pi$
$878$	5.34880	+	1.57055i	0.180513	+	0.0530035i
$879$	−11.1802	−	12.9026i	−0.377099	−	0.435195i
$880$	0.637606	−	0.187218i	0.0214937	−	0.00631112i
$881$	−44.2013	−	28.4064i	−1.48918	−	0.957038i	−0.996209	−	0.0869915i	$-0.972275\pi$
$881$	−44.2013	−	28.4064i	−1.48918	−	0.957038i	−0.492970	−	0.870046i	$-0.664089\pi$
$882$	5.32875	−	11.6683i	0.179428	−	0.392893i
$883$	10.7972	−	12.4607i	0.363356	−	0.419336i	−0.544405	−	0.838822i	$-0.683245\pi$
$883$	10.7972	−	12.4607i	0.363356	−	0.419336i	0.907761	+	0.419487i	$0.137790\pi$
$884$	9.81658	−	6.30874i	0.330167	−	0.212186i
$885$	2.41216	+	16.7769i	0.0810837	+	0.563950i
$886$	2.78631	+	19.3792i	0.0936078	+	0.651057i
$887$	−22.1023	+	14.2043i	−0.742121	+	0.476933i	−0.856268	−	0.516531i	$-0.827223\pi$
$887$	−22.1023	+	14.2043i	−0.742121	+	0.476933i	0.114147	+	0.993464i	$0.463587\pi$
$888$	8.39700	−	9.69065i	0.281785	−	0.325197i
$889$	−1.03878	+	2.27460i	−0.0348394	+	0.0762877i
$890$	114.294	+	73.4525i	3.83115	+	2.46213i
$891$	−0.0261978	+	0.00769236i	−0.000877659	+	0.000257704i
$892$	65.9461	+	76.1058i	2.20804	+	2.54821i
$893$	−43.1114	−	12.6587i	−1.44267	−	0.423606i
$894$	−3.02184	−	6.61691i	−0.101066	−	0.221303i
$895$	−11.9270	+	82.9543i	−0.398676	+	2.77286i
$896$	−21.1059			−0.705099
$897$	−0.992014	+	2.83973i	−0.0331224	+	0.0948158i
$898$	17.9885			0.600284
$899$	0.253592	−	1.76377i	0.00845778	−	0.0588252i
$900$	20.5249	+	44.9433i	0.684164	+	1.49811i
$901$	7.59768	+	2.23088i	0.253115	+	0.0743214i
$902$	0.450338	+	0.519718i	0.0149946	+	0.0173047i
$903$	4.33421	−	1.27264i	0.144234	−	0.0423508i
$904$	71.6403	+	46.0404i	2.38272	+	1.53128i
$905$	43.6398	−	95.5577i	1.45063	−	3.17645i
$906$	−3.39995	+	3.92375i	−0.112956	+	0.130358i
$907$	32.9483	−	21.1746i	1.09403	−	0.703091i	0.136274	−	0.990671i	$-0.456487\pi$
$907$	32.9483	−	21.1746i	1.09403	−	0.703091i	0.957757	+	0.287580i	$0.0928508\pi$
$908$	−3.75791	−	26.1368i	−0.124711	−	0.867381i
$909$	−1.89983	−	13.2136i	−0.0630133	−	0.438267i
$910$	7.40559	−	4.75928i	0.245493	−	0.157769i
$911$	−17.4784	+	20.1712i	−0.579086	+	0.668301i	−0.967408	−	0.253223i	$-0.918509\pi$
$911$	−17.4784	+	20.1712i	−0.579086	+	0.668301i	0.388322	+	0.921524i	$0.373055\pi$
$912$	−12.4697	+	27.3048i	−0.412912	+	0.904152i
$913$	−0.196801	−	0.126476i	−0.00651315	−	0.00418575i
$914$	−10.7546	+	3.15785i	−0.355732	+	0.104452i
$915$	−12.2775	−	14.1690i	−0.405882	−	0.468413i
$916$	−56.9928	−	16.7346i	−1.88310	−	0.552927i
$917$	−3.39541	−	7.43490i	−0.112126	−	0.245522i
$918$	1.54152	−	10.7215i	0.0508779	−	0.353863i
$919$	25.3453			0.836064			0.418032	−	0.908432i	$-0.362720\pi$
$919$	25.3453			0.836064			0.418032	+	0.908432i	$0.362720\pi$
$920$	−56.3420	−	98.2400i	−1.85754	−	3.23888i
$921$	−22.0577			−0.726825
$922$	−8.60376	+	59.8404i	−0.283350	+	1.97074i
$923$	1.88268	+	4.12249i	0.0619691	+	0.135694i
$924$	−0.155731	−	0.0457269i	−0.00512319	−	0.00150430i
$925$	16.5046	+	19.0473i	0.542666	+	0.626270i
$926$	−7.92795	+	2.32786i	−0.260529	+	0.0764981i
$927$	7.95167	+	5.11023i	0.261167	+	0.167842i
$928$	−5.27633	+	11.5535i	−0.173204	+	0.379264i
$929$	5.35859	−	6.18415i	0.175810	−	0.202895i	−0.661005	−	0.750382i	$-0.729870\pi$
$929$	5.35859	−	6.18415i	0.175810	−	0.202895i	0.836815	+	0.547486i	$0.184415\pi$
$930$	4.13550	−	2.65772i	0.135608	−	0.0871501i
$931$	3.63287	+	25.2672i	0.119063	+	0.828099i
$932$	−8.70175	−	60.5220i	−0.285035	−	1.98246i
$933$	4.58506	−	2.94664i	0.150108	−	0.0964687i
$934$	22.6495	−	26.1389i	0.741115	−	0.855292i
$935$	0.198233	−	0.434070i	0.00648292	−	0.0141956i
$936$	3.07252	+	1.97459i	0.100428	+	0.0645414i
$937$	−26.8166	+	7.87408i	−0.876061	+	0.257235i	−0.688691	−	0.725055i	$-0.741815\pi$
$937$	−26.8166	+	7.87408i	−0.876061	+	0.257235i	−0.187370	+	0.982289i	$0.559996\pi$
$938$	−10.0387	−	11.5853i	−0.327775	−	0.378272i
$939$	29.3916	+	8.63016i	0.959159	+	0.281634i
$940$	−65.3305	−	143.054i	−2.13085	−	4.66590i
$941$	4.68100	−	32.5571i	0.152596	−	1.06133i	−0.759250	−	0.650799i	$-0.774434\pi$
$941$	4.68100	−	32.5571i	0.152596	−	1.06133i	0.911846	−	0.410532i	$-0.134657\pi$
$942$	−48.7210			−1.58742
$943$	27.9900	−	39.0677i	0.911480	−	1.27222i
$944$	−25.0841			−0.816418
$945$	0.794723	−	5.52742i	0.0258523	−	0.179807i
$946$	0.0935148	+	0.204769i	0.00304043	+	0.00665761i
$947$	−19.2462	−	5.65120i	−0.625418	−	0.183639i	−0.0463589	−	0.998925i	$-0.514762\pi$
$947$	−19.2462	−	5.65120i	−0.625418	−	0.183639i	−0.579059	+	0.815286i	$0.696580\pi$
$948$	4.26561	+	4.92278i	0.138541	+	0.159884i
$949$	3.59354	−	1.05516i	0.116651	−	0.0342519i
$950$	−121.036	−	77.7854i	−3.92694	−	2.52369i
$951$	−0.297221	+	0.650823i	−0.00963805	+	0.0211044i
$952$	22.6304	−	26.1169i	0.733456	−	0.846454i
$953$	24.5517	−	15.7784i	0.795308	−	0.511113i	−0.0787738	−	0.996893i	$-0.525100\pi$
$953$	24.5517	−	15.7784i	0.795308	−	0.511113i	0.874082	+	0.485779i	$0.161464\pi$
$954$	0.657190	+	4.57086i	0.0212773	+	0.147987i
$955$	−4.78418	−	33.2747i	−0.154812	−	1.07674i
$956$	73.8555	−	47.4640i	2.38866	−	1.53510i
$957$	0.0660587	−	0.0762358i	0.00213538	−	0.00246435i
$958$	24.1527	−	52.8870i	0.780338	−	1.70870i
$959$	−9.32981	−	5.99591i	−0.301275	−	0.193618i
$960$	13.0840	−	3.84181i	0.422284	−	0.123994i
$961$	20.1483	+	23.2524i	0.649947	+	0.750078i
$962$	3.33068	+	0.977975i	0.107385	+	0.0315312i
$963$	−5.72839	−	12.5434i	−0.184595	−	0.404206i
$964$	−4.79680	+	33.3625i	−0.154494	+	1.07453i
$965$	68.8033			2.21486
$966$	−0.837549	+	16.5769i	−0.0269477	+	0.533355i
$967$	−48.3376			−1.55443			−0.777216	−	0.629233i	$-0.783369\pi$
$967$	−48.3376			−1.55443			−0.777216	+	0.629233i	$0.783369\pi$
$968$	−9.11517	+	63.3974i	−0.292973	+	2.03767i
$969$	8.95445	+	19.6075i	0.287658	+	0.629884i
$970$	−21.1708	−	6.21629i	−0.679752	−	0.199593i
$971$	23.1379	+	26.7026i	0.742532	+	0.856927i	0.993822	−	0.110985i	$-0.0354004\pi$
$971$	23.1379	+	26.7026i	0.742532	+	0.856927i	−0.251291	+	0.967912i	$0.580855\pi$
$972$	4.14200	−	1.21620i	0.132855	−	0.0390097i
$973$	8.89689	+	5.71768i	0.285221	+	0.183301i
$974$	−12.1439	+	26.5914i	−0.389115	+	0.852042i
$975$	−4.70106	+	5.42531i	−0.150554	+	0.173749i
$976$	23.3417	−	15.0008i	0.747149	−	0.480163i
$977$	1.79485	+	12.4835i	0.0574224	+	0.399382i	0.998180	+	0.0603022i	$0.0192064\pi$
$977$	1.79485	+	12.4835i	0.0574224	+	0.399382i	−0.940758	+	0.339079i	$0.889884\pi$
$978$	−8.39040	−	58.3565i	−0.268295	−	1.86604i
$979$	0.306178	−	0.196769i	0.00978550	−	0.00628876i
$980$	−58.5103	+	67.5244i	−1.86904	+	2.15699i
$981$	−3.39121	+	7.42572i	−0.108273	+	0.237085i
$982$	64.2114	+	41.2662i	2.04907	+	1.31686i
$983$	−11.0543	+	3.24584i	−0.352577	+	0.103526i	−0.453225	−	0.891396i	$-0.649727\pi$
$983$	−11.0543	+	3.24584i	−0.352577	+	0.103526i	0.100648	+	0.994922i	$0.467908\pi$
$984$	−38.2134	−	44.1007i	−1.21820	−	1.40588i
$985$	−52.8304	−	15.5124i	−1.68332	−	0.494266i
$986$	16.6242	+	36.4019i	0.529422	+	1.15927i
$987$	−1.76050	+	12.2446i	−0.0560375	+	0.389749i
$988$	−13.5423			−0.430837
$989$	12.3943	−	9.68930i	0.394116	−	0.308102i
$990$	0.278289			0.00884460
$991$	−3.57914	+	24.8934i	−0.113695	+	0.790766i	0.850577	+	0.525851i	$0.176253\pi$
$991$	−3.57914	+	24.8934i	−0.113695	+	0.790766i	−0.964272	+	0.264915i	$0.914656\pi$
$992$	0.688812	+	1.50829i	0.0218698	+	0.0478882i
$993$	26.8871	+	7.89475i	0.853235	+	0.250532i
$994$	16.3765	+	18.8995i	0.519431	+	0.599456i
$995$	−49.9541	+	14.6679i	−1.58365	+	0.465002i
$996$	31.1151	+	19.9965i	0.985921	+	0.633613i
$997$	−5.65570	+	12.3843i	−0.179118	+	0.392214i	−0.977800	−	0.209539i	$-0.932804\pi$
$997$	−5.65570	+	12.3843i	−0.179118	+	0.392214i	0.798682	+	0.601753i	$0.205531\pi$
$998$	−57.4009	+	66.2442i	−1.81699	+	2.09692i
$999$	1.85247	−	1.19051i	0.0586095	−	0.0376660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.b.31.1	✓	10
3.2	odd	2		207.2.i.a.100.1		10
23.3	even	11	inner	69.2.e.b.49.1	yes	10
23.7	odd	22		1587.2.a.r.1.1		5
23.16	even	11		1587.2.a.q.1.1		5
69.26	odd	22		207.2.i.a.118.1		10
69.53	even	22		4761.2.a.bm.1.5		5
69.62	odd	22		4761.2.a.bp.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.31.1	✓	10	1.1	even	1	trivial
69.2.e.b.49.1	yes	10	23.3	even	11	inner
207.2.i.a.100.1		10	3.2	odd	2
207.2.i.a.118.1		10	69.26	odd	22
1587.2.a.q.1.1		5	23.16	even	11
1587.2.a.r.1.1		5	23.7	odd	22
4761.2.a.bm.1.5		5	69.53	even	22
4761.2.a.bp.1.5		5	69.62	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.357685 - 2.48775i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-4.14200 - 1.21620i) q^{4} +(2.65565 + 3.06479i) q^{5} +(-2.41153 + 0.708089i) q^{6} +(-1.15843 - 0.744479i) q^{7} +(-2.41899 + 5.29684i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.357685 - 2.48775i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-4.14200 - 1.21620i) q^{4} +(2.65565 + 3.06479i) q^{5} +(-2.41153 + 0.708089i) q^{6} +(-1.15843 - 0.744479i) q^{7} +(-2.41899 + 5.29684i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(8.57432 - 5.51038i) q^{10} +(-0.00388573 - 0.0270259i) q^{11} +(0.614354 + 4.27292i) q^{12} +(-0.527646 + 0.339098i) q^{13} +(-2.26643 + 2.61561i) q^{14} +(1.68463 - 3.68882i) q^{15} +(5.04885 + 3.24470i) q^{16} +(4.13515 - 1.21419i) q^{17} +(1.64589 + 1.89945i) q^{18} +(-4.79898 - 1.40911i) q^{19} +(-7.27232 - 15.9241i) q^{20} +(-0.195972 + 1.36301i) q^{21} -0.0686236 q^{22} +(1.11722 + 4.66388i) q^{23} +5.82306 q^{24} +(-1.62885 + 11.3289i) q^{25} +(0.654861 + 1.43394i) q^{26} +(0.959493 + 0.281733i) q^{27} +(3.89279 + 4.49252i) q^{28} +(-3.54487 + 1.04087i) q^{29} +(-8.57432 - 5.51038i) q^{30} +(-0.200359 + 0.438726i) q^{31} +(2.25133 - 2.59818i) q^{32} +(-0.0229694 + 0.0147615i) q^{33} +(-1.54152 - 10.7215i) q^{34} +(-0.794723 - 5.52742i) q^{35} +(3.63158 - 2.33387i) q^{36} +(1.44203 - 1.66419i) q^{37} +(-5.22204 + 11.4347i) q^{38} +(0.527646 + 0.339098i) q^{39} +(-22.6577 + 6.65289i) q^{40} +(-6.56243 - 7.57345i) q^{41} +(3.32075 + 0.975060i) q^{42} +(-1.36272 - 2.98394i) q^{43} +(-0.0167742 + 0.116667i) q^{44} -4.05529 q^{45} +(12.0022 - 1.11118i) q^{46} +8.98345 q^{47} +(0.854114 - 5.94049i) q^{48} +(-2.12019 - 4.64257i) q^{49} +(27.6009 + 8.10436i) q^{50} +(-2.82227 - 3.25707i) q^{51} +(2.59792 - 0.762819i) q^{52} +(1.54567 + 0.993342i) q^{53} +(1.04408 - 2.28621i) q^{54} +(0.0725093 - 0.0836802i) q^{55} +(6.74562 - 4.33514i) q^{56} +(0.711799 + 4.95067i) q^{57} +(1.32148 + 9.19107i) q^{58} +(-3.51609 + 2.25965i) q^{59} +(-11.4641 + 13.2303i) q^{60} +(1.92053 - 4.20538i) q^{61} +(1.01978 + 0.655371i) q^{62} +(1.32125 - 0.387954i) q^{63} +(2.20204 + 2.54129i) q^{64} +(-2.44051 - 0.716597i) q^{65} +(0.0285073 + 0.0624222i) q^{66} +(-0.630353 + 4.38420i) q^{67} -18.6045 q^{68} +(3.77831 - 2.95371i) q^{69} -14.0351 q^{70} +(1.02832 - 7.15212i) q^{71} +(-2.41899 - 5.29684i) q^{72} +(-5.72936 - 1.68229i) q^{73} +(-3.62430 - 4.18266i) q^{74} +(10.9818 - 3.22454i) q^{75} +(18.1636 + 11.6731i) q^{76} +(-0.0156188 + 0.0342005i) q^{77} +(1.03232 - 1.19136i) q^{78} +(1.26938 - 0.815780i) q^{79} +(3.46368 + 24.0904i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-21.1882 + 13.6168i) q^{82} +(5.61081 - 6.47522i) q^{83} +(2.46941 - 5.40726i) q^{84} +(14.7027 + 9.44888i) q^{85} +(-7.91074 + 2.32280i) q^{86} +(2.41940 + 2.79213i) q^{87} +(0.152551 + 0.0447931i) q^{88} +(5.53741 + 12.1252i) q^{89} +(-1.45052 + 10.0886i) q^{90} +0.863693 q^{91} +(1.04468 - 20.6766i) q^{92} +0.482312 q^{93} +(3.21325 - 22.3486i) q^{94} +(-8.42581 - 18.4500i) q^{95} +(-3.29862 - 0.968563i) q^{96} +(-1.41765 - 1.63606i) q^{97} +(-12.3079 + 3.61394i) q^{98} +(0.0229694 + 0.0147615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Introduction

L-functions

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